The BS in Applied Statistics Program

 

Minimum Requirement for the degree of BS in Applied Statistics 127 credits.

A student must accumulate a minimum of 127 credit hours, with a minimum of the indicated numbers of credit hours from sections I-IV, in order to obtain the degree. The sections and the indicated required credit hours are as the following.

Section Description Credit Hours
I Language and General Education Requirements 21
II Mathematics & Economics  15
III Applied Statistics Core
Courses
91
Total 127

Section I. General Education Requirements (21 Credit Hours)

Section I A: Compulsory General Education Courses (Three courses: 9 credit hours)

Section I B: Optional General Education Courses (2 courses, OPT001 and OPT002).

For Applied Statistics, students should choose Gen 239 and one more course from the following list; a total of 3+3=6 Credit Hours.   

Section I C: Optional Courses from Business & Relevant Subject (2 courses, OPT003 and OPT004). Applied Statistics students may choose any two courses: 3+3=6 credit hours).

Section II: Mathematics and Economics  (15 Credit Hours)

These courses stress the fundamental principles upon which the applied statistics subject is based. Applied Statistics students must take a total of 15 credit hours).

Course Number/Course title Credit Hours
MAT101: Differential & Integral Calculus 3
MAT 102: Differential Equations & Special Functions 3
MAT 206: Basic Algebra and Linear Algebra 3
ECO101:  Principles of Microeconomics 3
ECO102: Introduction to Macroeconomics 3
Total 15

Section III. Applied Statistics Core Courses (91 Credit Hours)

The following courses stress fundamental Applied Statistics concepts.

Course No. Course Title Credits
AST – 101 Introduction to Statistics 3
AST – 102 Elements of Probability 3
AST – 201 Probability Distributions 3
AST – 202 Sampling Distributions 3
AST – 203 Statistical Inference I 3
AST – 204 Agricultural Statistics and Design of Experiments 3
AST – 205 Introduction to Demography 3
AST – 206 Introductory Sampling Methods 3
AST – 207 Applied Statistical Analysis with R (Lab) 3
AST – 301 Design and Analysis of Factorial Experiments 3
AST – 302 Advanced Sampling Techniques 3
AST – 303 Statistical Inference II 3
AST – 304 Applied Regression Analysis 3
AST – 305 Introduction to Epidemiology 3
AST – 306 Population Studies 3
AST – 307 Social Statistics and Social Development 3
AST – 308 Statistical Analysis Using SPSS and SAS (Lab) 3
AST – 309 Applied Nonparametric Statistics 3
AST – 310 Categorical Data Analysis 3
AST – 401 Advanced Probability and Stochastic Process 3
AST – 402 Research Methodology 4
AST – 403 Applied Multivariate Data Analysis 3
AST – 404 Survival Analysis I 3
AST – 405 Industrial Statistics and Operation Research 3
AST – 406 Modeling Time Series Data 3
AST – 407 Introduction to Generalized Linear Models 3
AST – 408 Life Contingencies I 3
AST – 409 Bayesian Inference and Decision Theory 3
AST – 410 Statistical Analysis using STATA (Lab) 3
AST – 499 Project Report and Seminar 3
  Total 91

AST-101
Description

Statistics and its origin:
Defining Statistics, Characteristics of Statistics, Uses & Importance of Statistics, Population & Sample, Sources of Statistical Data, Parameter and Statistic
Summarizing Data:
Meaning of Data, Level of Measurement, Variable and attribute, Summarizing and Presenting Data, Frequency Distribution, Formation of Discrete and Continuous Frequency Distribution, Cumulative Frequency Distribution, Presenting Data by Graphs and Diagrams, Presentation of Qualitative Data, Presentation of Quantitative Data.
Descriptive Statistics I: Measures of Central Tendency
Measures of central tendency, arithmetic mean, median, quartiles, percentiles and deciles, mode, geometric mean, harmonic mean, other measures of average, comparing the averages, properties of measures, effects of change in origin and scale, stem and leaf plot
Descriptive Statistics II: Measures of Dispersion
Meaning of dispersion, measures of dispersion, absolute measures of dispersion, relative measures of dispersion, empirical relations among measures of dispersion, comparing the measures, moments, central moments in terms of raw moments, effects of change in origin and scale on moments, Sheppard’s correction for moments, shape characteristics of a distribution, box and whisker plots.
Simple Linear Regression and Correlation:
Correlation analysis, measuring the correlation, rank correlation, regression analysis, simple linear regression model, scatter diagram, Least- square method, properties of regression coefficient, partitioning of the total variation in regression, Coefficient of multiple determination

Credits 3

AST-102
Description

Mathematical logic: propositional calculus, predicate calculus. Set theory: sets, relations, partial ordered sets, functions. Counting: Permutations, Combinations, principles of inclusion and exclusion. Discrete Probability. Algorithm and Growth of functions. Mathematical reasoning: induction, contradiction, recursion. Recurrence Relations. Graph theory: graphs, paths, trees. Algebraic structures: binary operations, semi groups, groups, permutation groups, rings and fields, lattices.

Credits 3
 

Description

Credit-3

  • Random variables; probability mass function, cumulative density function and probability density function
  • Discrete Probability Distributions: Bernoulli, binomial, Poisson, geometric, negative binomial, Hypergeometric, uniform
  • Continuous Probability Distributions: uniform, exponential, gamma, beta, normal, log- normal,Weibull
  • Identification of Moment and cumulant generating functions; characteristic function of discrete and continuous distributions
  • Showing moments from Moment and cumulant generating functions; characteristic function
  • Distribution of a function of a random variable from the distribution of a random variable
  • Determination of probability generating function of discrete and integer-valued random variables
  • Application of PGF, MGF, CGF and cumulants and the reason of their use
  • Joint, Marginal and conditional distributions
  • Law of large numbers; and central limit theorem.
  • Cauchy-Schwartz, Markov and Chebysheb inequality
Credits 3
Pre-requisite MAT101, AST-101, AST-102

AST-203
Description
Credit-3
Methods of finding estimators: methods of moments, maximum likelihood, and other methods;
Properties of point estimators: closeness, mean-squared error, loss and risk functions;
Sufficiency: sufficient statistics, factorization criterion, minimal sufficient statistics, ancillary statistics;
Completeness: complete statistics, exponential family;
Likelihood Functions
Parameter Estimation(point and interval):
Linear estimation
Maximum Likelihood estimation
Bayesian estimation
Large sample properties and procedures
Empirical distribution function
Introduction to test of hypothesis : Best critical region, Most powerful tests, Concept of confidence interval, Confidence interval for parameters

Credits 3
Pre-requisite AST-101, AST-102

AST-204
Description

Agricultural statistics: definition and application; basic and current agricultural statistics; estimation of mean yields; crop cutting experiment; crop forecasting; livestock; sample survey.

Census of agriculture: objectives; scope; coverage; concepts and definitions. Statistics of selected agricultural crops; index number of agricultural production; weights, indices used;

Design of experiments: some typical examples of experimental design; basic principles;

the analysis of variance; analysis of fixed effects, random effect and mixed effect model; estimation of model parameters; unbalanced data; model adequacy checking; regression model, comparisons among treatment means, graphical comparisons of means, contrasts, orthogonal contrasts, multiple testing, Scheffe’s method, comparing pairs of treatment means, comparing treatment means with a control; Determining sample size; operating characteristic curve, least squares estimation of the model parameters, normality test.
Complete randomize design(CRD), Randomized blocks design (RBD), Latin squares design (LSD), model adequacy checking; estimating model parameters; Gareco-Latin square design; balanced incomplete block design (BIBD); statistical analysis of BIBD; Least- squares estimation of BIBD; example of real life application of these methods.

Credits 3
Pre-requisite AST-203

AST-205
Description

Introduction: Basic concept of demography; Role and importance of demographic/population studies; Sources of demographic data: census, vital registration system, sample surveys, population registers and other sources especially in Bangladesh.
History: History of census taking and vital registration in the sub-continent, Uses of data from these sources; strength and weakness of data from them, Growth of population in Bangladesh since 1901.
Errors in demographic data: types of errors and methods of testing the accuracy of demographic data, Quality checking and adjustment of population data. Post enumeration check (PEC) and detection of errors and deficiencies in data and the needed adjustments and corrections.
Fertility: Basic measures of fertility. Crude birth rate, age specific fertility rates (ASFR), general fertility rate (GFR), total fertility rate (TFR), gross reproduction rate (GRR) and net reproduction rate (NRR), child-woman ratio, Concept of fecundity and its relationship with fertility.
Demographic theory:Transition theory and the present situation in Bangladesh, Malthus’ theory and its criticism. Mortality: Basic measures of mortality: crude death rate (CDR), age specific death rates (ASDR), infant mortality rate, child mortality rate, neo-natal mortality rate, Standardized death rate its need and use, Direct and indirect standardization of rates, Commonly used ratios: Sex ratio, child-woman ratio, dependency ratio, density of population.
Fertility and mortality in Bangladesh since 1951: Reduction in fertility and mortality in Bangladesh in recent years, Role of socio-economic development on fertility and mortality.
Nuptiality: Marriage, types of marriage, age of marriage, age at marriage and its effect on fertility, celibacy, widowhood, divorce and separation, their effect on fertility and population growth.

Migration: Definition, internal and international migration, Sources of migration data, Factors affecting both internal and international migration, laws of migration. Impact of migration on origin and destination, its effect on population growth, age and sex structure, labor supply, employment and unemployment, wage levels, and other socio-economic effects, Migration of Bangladeshis abroad and its impact on overall economic development of the country.

Credits 3
Pre-requisite AST-101

AST-206
Description

Introduction: Uses of Sample Surveys and some review of sampling design of national surveys of Bangladesh, Preliminary Planning of a Sample Survey. Different types of errors associated with sampling and complete enumeration. Declining Coverage and Response Rates, Sampling Weights, questionnaire, Design effect with real life application, sample size determination.
The Population and the Sample: The Population, Elementary Units, Population Parameters, The Sample, Probability and Nonprobability Sampling, Sampling Frames, Sampling Units, and Enumeration Units, Characteristics of Estimates of Population Parameters, Bias, Mean Square Error, Validity, Reliability, and Accuracy.
Simple Random Sampling: How to Take and apply Simple Random Sample. Estimation of Population Characteristics and Standard Errors
Systematic Sampling: How to Take and apply Systematic Sampling, Estimation of Population Characteristics, Sampling Distribution of Estimates, Variance of Estimates, A Modification That Always Yields Unbiased Estimates.
Stratification and Stratified Random Sampling: How to Take and apply Stratified Random Sample , Population Parameters for Strata, Sample Statistics for Strata, Estimation of Population Parameters from Stratified Random Sampling, Estimation of Standard Errors, Allocation of Sample to Strata, Equal Allocation, Proportional Allocation: Self-Weighting Samples, Optimal Allocation, Stratification After Sampling.
Ratio Estimation and Regression Estimation: How to apply through Real life scenarios. Approximation to the Standard Error of the Ratio Estimated Total, Determination of Sample Size, Regression Estimation of Totals.
Cluster Sampling: Real life application of cluster sampling. Simple One-Stage Cluster Sampling, Two-Stage Cluster Sampling: Clusters Sampled with Equal Probability, Choosing the Optimal Cluster Size n Considering Costs, Cluster Sampling Unequal Probability: Probability Proportional to Size Sampling, the Horvitz–Thompson Estimator, the Hansen–Hurwitz Estimator

Credits 3
Pre-requisite AST-203

AST-207
Description

A first session in R

  • Getting data into R
  • Basic data manipulation
  • Data Modeling
  • Distribution fitting
  • Basic plotting
  • Loops and functions
  • Basic stats
  • Survival Model
  • Advanced data manipulation

 

Credits 3
Pre-requisite AST-203

AST-301
Description

Introduction to Factorial Designs: Basic definition and principles; The advantage of factorials; The two-factor factorial design; statistical analysis of fixed effects model, model adequacy checking, estimating the model parameters, choice of sample size, the assumption of no interaction in a two-factor model, one observation per cell; The general factorial design; Fitting response curve and surfaces; Blocking in a factorial design.

Response Surface Methods: basic concept of response surface methodology.

Experiments with Random Factors: The two-factor factorial with random factors; The two-factor mixed model; Sample size determination with random effects; Rules for expected mean squares; Approximate F tests; Approximate confidence intervals on variance components; The modified large-sample method; Maximum likelihood estimation of variance components.
Nested and Split-Plot Designs: The two-stage nested designs; statistical analysis, diagnostic checking, variance components; General m-staged nested design; Designs with both nested and factorial factors; The split-plot design;
Analysis of Covariance: Description of the procedure; Factorial experiments with covariates.

Credits 3
Pre-requisite AST-204

AST-302
Description

Sampling with real life application of unequal clusters with unequal probability with and without replacement different selection methods: PPS selection, Raj’s, Murthy’s and Rao-Hartley-Cochran methods of selection, Two-stage sampling with equal and unequal sized clusters-estimates and standard errors; estimation for proportions; stratified two-stage sampling.
Multistage sampling: how to apply different two and three stage sampling schemes; the concept of self-weighting estimates; assumptions for self-weighting estimates;
Multiphase sampling: real life application of this technique. Two-phase or double sampling; ratio and regression estimators for double sampling and respective standard errors; double sampling for stratification. Repeated sampling; sampling from the same population on two occasions, more than two occasions. Interpenetrating sub sampling. Concept of base line survey and panel survey.
Special sampling schemes: capture-recapture method; network sampling; snowball sampling; adaptive cluster sampling; rank set sampling with application.
Re-sampling methodologies: bootstrap, Jackknife and Gibbs sampling.
Sampling and non-sampling errors: sources and types of non-sampling error; non-sampling bias; non-response error; control of non-response; techniques for adjustments of non-response; Politz-Simon’s technique; response bias and response variance.

Credits 3
Pre-requisite AST-206

AST-303
Description

Introduction to test of hypothesis
Best critical region

  • Most powerful tests
  • Likelihood ratio tests
  • Exponential family of densities
  • Sufficiency and exponential family of densities and tests
  • Sequential probability ratio test
  • Theory of confidence intervals and tests
  • Goodness of fit tests
  • Tests based on quasi-likelihood
  • Bayesian inference
  • Asymptotic distribution of LRTs and other large sample tests
Credits 3
Pre-requisite AST-203

AST-304
Description

  1. Simple Linear Regression Model
  • Model for E(Y|X), model for distribution of errors
  • Least- squares estimation
  • Estimation of variance
  1. Inferences for Simple Linear Model
  • Inferences concerning the slope (confidence intervals and t-test)
  • Confidence interval estimate of the mean Y at a specific X
  • Prediction interval for a new Y
  • Analysis of Variance partitioning of variation in Y
  • R-squared calculation and interpretation
  1. Diagnostic procedures for aptness of model
  • Residual analyses

o Plots of residuals versus fits, residuals versus x

o Tests for normality of residuals

o Lack of Fit test, Pure Error, Lack of Fit concepts

  • Transformations as solution to problems with the model
  1. Matrix Notation and Literacy
  • X matrix, vector, y vector, vector
  • (X’X)-1 X’Y estimates coefficient vector
  • Variance- Covariance matrix
  1. Multiple Regression Models and Estimation
  • extension to simple linear model
  • Interaction models
  • Basic estimation and inference for multiple regression
  • Generalized Least- Squares and Weigthed Least- Squares
  • Extra Sum of Squares Principles and related Tests
  1. Multicollinearity and Model diagnostics
  2. Selecting the Best Regression Equations
Credits 3
Pre-requisite AST-203, MAT206

AST-305
Description

Introduction: Measuring Disease Frequency, Problems of Validity, Problems in controlling for extraneous factors
Fundamentals of Epidemiologic Research: Epidemiologic Research, Etiologic Research
Types of Epidemiological Research: Experiments, Quasi Experiments, Observational Studies
Design Options in Observational Studies: Subject selection, Methods of observation
Typology of observational Basic Designs: Cohort study, cross-sectional study, case-control study, Hybrid designs, incomplete designs
Measures of Disease Frequency: Basic incidence measures; risk and rate, Estimation of average rates, Estimation of risk, Prevalence measures, Mortality measures
Measures of Association: Ratio measures, Difference measures,
Confounding: Working definition of a confounder, risk factors, single risk factor confounding; Confounding involving several risk factors; definition of joint confounding, variable selection and control of confounding.
Measures of Potential Impact and Summary of measures: Measures of potential Impact, Summary of epidemiologic measures
Validity of Epidemiologic Research: Validity and precision, Internal validity

Credits 3
Pre-requisite AST-203, AST-304

AST- 306
Description

Adjustment of demographic data: Sources and types of errors and deficiencies in data; General methods of evaluation and detection of error and deficiencies in data; Methods of checking completeness and other types of errors in demographic data and their adjustment.
Graduation of data: Meaning and its need, techniques of graduation, graduation of age distribution.
Life table: Its concept, structure and calculation, complete life table (life table by single year of age) and abridged life table, multiple decrement life tables, working life table, different life table functions and inter-relationships among them, use of life table, etc.
Force of mortality: Idea and definition calculation of life table with the help of force of mortality. Population growth, techniques to measure it, doubling time concept in demography. Population estimates and projections. Different techniques of population projection- component method, arithmetic/linear method, geometric method, exponential method, matrix method, etc., need of population projections.
Stable and stationary population, their characteristics and uses, Lotka’s characteristics equation, intrinsic birth and death rates, effect of uniform drop in force of mortality on the growth rate, effects of changes in fertility and mortality on the age distribution of population. Model life tables, Coale and Demeney regional model life tables.
Population in Bangladesh: History of growth of population in Bangladesh; Implications of the growth of population in Bangladesh; Population policy in Bangladesh; Level, trends and determinants in fertility, mortality and migration in Bangladesh; Interrelationship between population and development; Future prospects of population and population control in Bangladesh; Aged and aging of population in Bangladesh

Credits 3
Pre-requisite AST-205

AST- 307
Description

National income: Concepts, Measurement and Problems; Social Accounting Matrix. Income Distribution and Wealth: Causes of Concentration; Meaning of Inequality; Measures of Inequality; Frequency of Income; Lorenz Curve of Income; Gini coefficient; Atkinson’s index, etc.
Poverty: Conceptual issues of Poverty; Measurement of Different Poverty Indices.
Introduction to Psychometrics: Measurement in Psychology and Education; Intelligent and Achievement tests; Test scores; Equivalence of Scores; Z-score and T-score; Intelligent Quotient.
Definition, Nature and Importance of Anthropology; Role and Functions of Family
Social inequality: Inequality by Sex, Age, Rank, Caste, Race, Class, Power, Rule and Social Connections.
Social Sector Development Policies: Development in Agriculture, Industry (a) Growth Performance, Outlay and Yield (b) Agrarian Structure and Its changes (c) Plan Outlay; Rural Development; Human Development; Women and Youth Development; Land Reforms in Bangladesh; InfrAST-ructure Development; ADP allocation to social sectors; Fiscal Policies for Development.

Credits 3
Pre-requisite AST-205

AST- 308
Description

  • Brief knowledge in SPSS
  • Creating a data file in SPSS
  • Data Manipulation: Inserting variables, Inserting case, Merging files, case selection, selecting a random sample, aggregate data, splitting file, weight cases
  • Data Transformation
  • Categorize variables
  • Frequency distribution table
  • Measures of central tendency, measures of dispersion
  • Creating graphs and cross tables
  • Test of hypothesis
  • Correlation and regression

SAS Programming

  • Introduction to SAS
  • SAS Syntax
  • SAS Datasets
  • Reading SAS Datasets
  • Reading Delimited Raw Data
  • Manipulating Data
  • Validating and Cleaning Data
  • Combining SAS Data Sets
  • Compilation and Execution of the Data Step
  • Producing Summary Reports
  • Enhancing Reports
  • Basics of ODS
  • Processing Data Iteratively
  • Transforming variables
  • Basic Statistics Using SAS
  • Univariate Description and Inference
  • ProcUnivariate
  • Analysis of Variance
  • Categorical Data Analysis
  • Linear Regression
  • Logistic Regression
Credits 3
Pre-requisite AST-203, AST-204, AST-304

AST- 309
Description

  • Review of elementary probability contents
  • Foundational comparison of parametric and nonparametric approaches
  • Dichotomous data problem
  • General connection between confidence sets and hypothesis tests
  • General connection between point estimates and hypothesis tests
  • Goodness-of-fit Tests (Kolmogorov-Smirnov two-sample test for general differences, Run test)
  • Tests for a single location parameter
  • Test for several location parameters
  • Tests for scale parameters
  • Distribution tests
  • Measures of Association
  • Tests for Randomness trends
  • Nonparametric regression
  • Sign test and associated interval and point estimates for one-sample data
  • Signed rank test, interval and point estimates for one-sample data
  • Rank Correlation
  • Wilcoxon signed rank test
  • Wilcoxon sum rank test
  • Mann-Whitney U test
  • Kruskal-Wallis test
  • Asymptotic relative efficiency comparisons
  • Rank sum test, interval and point estimates for two-sample data
  • One-Way Layout: tests and multiple comparison procedures
  • Two-Way Layout: tests and multiple comparison procedures
  • Kendall’s tau procedures for independence of two random variables
Credits 3
Pre-requisite AST-303

Description

AST- 310

Introduction: Distributions and Inference for Categorical Data
Categorical Response Data; Distributions for Categorical Data; Statistical Inference for Categorical Data
Describing Contingency Tables
Probability Structure for Contingency Tables; Comparing Two Proportions; Partial Association in Stratified 2×2 Tables; Extensions for I×J Tables

Inference for Contingency Tables
Confidence Intervals for Association Parameters; Testing Independence in Two-Way Contingency Tables; Following-Up Chi-Square Tests; Two-Way Tables with Ordered Classifications.
Introduction to Generalized Linear Models
Generalized Linear Models for Binary Data and counts; Moments and Likelihood for Generalized Linear Models; Inference for Generalized Linear Models; Fitting Generalized Linear Models; Quasi-likelihood and Generalized Linear Models
Logistic Regression
Inference and Interpreting Parameters in Logistic Regression; Logit Models with Categorical Predictors; Fitting Logistic Regression Models

Credits 3
Pre-requisite MAT102, MAT206, AST-201

AST- 401
Description

  • Modern probability: probability as a set function; Borelfield and extension of probability measure
  • Probability measure notion of random variables; probability space; distribution function; expectations and moments
  • Convergence of random variables; Laplace transformation
  • Markov Chains: introduction, transition probability matrices of a Markov chain, First step analysis; some special Markov chains; Regular transition probability matrices
  • The classification of states; Basic limit theorem of Markov chain; Reducible Markov chains
  • Poisson process: the Poisson distribution, counting and Poisson process; the law of rare events
  • Continuous time Markov chains: pure birth processes; pure death processes; birth and death processes
  • Limiting behavior of birth and death processes; birth and death process with absorbing states; finite state continuous time Markov chains
  • Renewal theory and its applications : introduction, distribution of N(t), limit theorems and their applications
  • Renewal reward process regenerative process, semi Markov process, queing process
  • The connection between Poisson process and the Poisson distribution, Poisson process as
  1. the distribution of waiting between events
  2. the distribution of process increments

iii. the behavior of the process over an infinitesimal time interval

Credits 3
Pre-requisite NONE

AST- 402
Description

Introduction to Research: What is Research? Research Concepts, Concept, aims and objectives of research; types of research, steps involved in research, selection and formulation of research problems; proposal writing; examining the designs ofsome known researches
Questionnaire: Questionnaire, check lists, FGD guidelines etc.; preparation of questionnaires. Preparation of manuals for interviewer, Enumerators training, monitoring and supervision for controlling the quality of data; how to avoid non-response
Report writing: Report writing; content and organizations of the report; heading and subheadings; techniques of writing conclusion, summary, recommendations, footnotes references, appendix, Examining some local and international reports
The concept of monitoring and evaluation (M & E): Objectives, usefulness and scope of M & E. Views of different schools on M & E. Performance monitoring versus performance evaluation
Timing and type of M & E: Summative, formative, continuous, participatory, diagnostic, log frame, etc.; baseline, ongoing and end line evaluation; impact evaluation; M & E of ongoing programs (activities, inputs, outputs, effect); follow-up for remedies, and post programs evaluation
Monitoring and evaluation plan and data sources: Indicators for monitoring and evaluation, Identification of indicators and characteristics of ideal indicators; factors influencing indicator selection
Quantitative Research Methods: The Scientific Method, Design of Quantitative Surveys, Quantitative Research Methods—Wrap-Up
Qualitative Research: Introduction to Qualitative Research and Research Approaches, Qualitative Research Methods—The Toolkit, Data Analysis and Theory in Qualitative Research Articles
Reliability and Validity in Measurements: Initiation of model building, Measurement error, Test for sound measurement, Reliability and its measurements, Validity and its types, Measurements of validity; stability of the model over the population, Construction of measurements scales
Field trip, report writing and presentation on selected topics

Credits 4
Pre-requisite AST-302, AST-306

AST- 403
Description

  • Preliminaries of multivariate analysis: applications of multivariate techniques
  • The organization of data; data display and pictorial representations; distance
  • Random vectors and random sampling: some basic of matrix and vector algebra; positive Definite matrices; a square-root matrix; random vectors and matrices; mean vectors and covariance matrices; matrix inequalities and maximization
  • The multivariate normal distribution: the multivariate normal density and its properties
  • The multivariate marginal, conditional and joint probability distributions
  • Assessing the assumption of normality; detecting outliers and data cleaning; transformation to near normality
  • Inferences about a mean vector: the plausibility of mean vector as a value for a normal population mean; Hotelling T and likelihood ratio tests; confidence regions and simultaneous comparisons of component means
  • Large sample inference about a population mean vector; inferences about mean vectors when some observations are missing; time dependence in multivariate data
  • Comparisons of several multivariate means: paired comparisons and a repeated measures design; comparing mean vectors from two populations
  • Principal components: Introduction and concepts of principal components
  • Factor analysis: Introduction, The orthogonal factor model and methods of estimation
  • Canonical correlation analysis: Introduction and basic concepts
  • Discrimination and Classification: Introduction, separation and classification for two populations
  • Profiles analysis; repeated measures designs and growth curves
Credits 3
Pre-requisite MAT101, MAT206, AST-201, AST-303

AST- 404
Description

Basic Concepts & Models:
Introduction, lifetime distribution, continuous model, discrete model, hazard function, exponential distribution, Weibull distribution, log-normal distribution, log-logistic distribution, gamma distribution, regression models
Observation schemes, Censoring & Likelihood:
Types of censoring and maximum likelihood, Truncation
Some Nonparametric & Graphical Procedures:
Nonparametric estimation of a survivor function and quantiles, Non parametric methods for estimating survival function and variance of the estimator viz. Acturial and Kaplan- Meier methods product limit estimate, Nelson-Aalen estimate, plots involving survivor or cumulative hazard function, estimation of hazard or density function, methods for truncated and interval censored data, life tables
Inference Procedure for Parametric Models:
Inference procedure for exponential distribution, for gamma distribution, models with polynomial based hazard function, grouped, interval censored or truncated data
Parametric regression models:
Log-location scale regression model, proportional hazard regression model

Credits 3
Pre-requisite AST-201, AST-304, AST-305, AST-309

AST- 405
Description
Industrial Statistics: Fundamental concepts of industrial statistics, its purposes and real life application; industrial quality control.Total quality control; statistical quality control; chance and assignable causes of variation; statistical process control.
Control chart: concept of control chart; necessary steps for constructing control charts; types of control charts; p-chart; d-chart; c-chart; u-chart; R and S charts (control charts with standard given and control charts with no standard given);
Basic concepts of acceptance sampling; OC curve and its uses; types of OC curves; properties of OC curves.
Basic concepts of single sampling plan for attributes; constructed of type A and type B OC curves under the single sampling plan for attributes; specific points on the OC curve (AQL, LTPD); rectifying inspection; AOQ; AOQL; ATI; ASN; designing a single sampling plan;
Basic concepts of double sampling plan; introduction to multiple sampling plan and sequential sampling analysis;
Operations Research: Nature and impact of OR approach; phases of OR. Concept of linear programming problem (LPP); construction of LPP; Solution of LPP: graphical and the simplex method; revised simplex method; Big-M method, two phase method; concept of convergence, degeneracy and cycling.
Duality: dual primal relationship and formulation of dual problems.
Sensitivity analysis: introduction to sensitivity analysis.
Game theory: finite and infinite games; zero sum games; two person zero sum games; pay off matrix; maximum and minimum criterion of optimal solution of a game; dominance property;

Credits 3
Pre-requisite MAT101, AST-201

AST- 406
Description
Introduction:
Examples of time series, Objectives, Types of variation, Stationarity, Trends and Seasonal Components, No Seasonal Component, Trend and Seasonality, time plot
The autocovariance of a stationary time series:
Strict stationarity, applied to stationary time series, drawbacks of shift operator, backwards difference, the spectral density, Time series models, Box-Jenkins Model, concept of a filter, root characteristic equation of time series
Estimation of the mean and the autocovariance:
Estimation of Mean, Estimation autocovariance, Prediction, A short course in inference, Prediction of random variables, Prediction for stationary time series
The Wold decomposition and Partial correlation:
Partial autocorrelation, AR process, MA process, ARMA processes, Calculation of the ACVF, Prediction of an ARMA Process, conintegrated time series, ARIMA time series
Random Walk:
Concept and properties of discrete random walks and random walks with normally distributed increments, both with and without drift
Multivariate Autoregressive Model: Concept
Spectral analysis:
The spectral distribution, Spectral representation of a time series, Prediction in the frequency domain, Interpolation and detection, Estimation of the spectral density, the periodogram, Smoothing the periodogram, Linear filters
Forecasting:
Introduction, univariate procedures, multivariate procedures, comparative review of forecAST-ing procedures, prediction theory
Identification, Estimation and Diagnosis of a time series:
Criteria for choosing between models, diagnostic tests applied to residuals
Text: Makridakis, S., Wheelwright, C. and Hyndman, R.J. (1997). ForecAST-ing Methods and Application, 3rd Edition. Wiley

Credits 3
Pre-requisite AST-303, AST-304

AST- 407
Description
Generalized linear models: Exponential family of distributions; Properties of distributions in Exponential family,Component of GLM, Random systematic link function
Estimation: method of maximum likelihood, method of Least- squares, estimation of generalized linear models
Inference: sampling distribution for scores, sampling distribution for maximum likelihood estimators,
Confidence intervals for model parameters, adequacy of a model, sampling distribution for log-likelihood statistic, log-likelihood ratio statistic (deviance),assessing goodness of fit, hypothesis testing;
Multiple Regression: maximum likelihood estimation, log-likelihood ratio statistic;
Models for binary responses: probability distributions, generalized linear models, general logistic regression, maximum likelihood estimation and log-likelihood ratio statistic, other criteria for goodness of fit, leAST- square methods; Multinomial distributions; Nominal logistic regression models; Ordinal logistic regression models;
Models for count Data: probability distributions, log-linear models, maximum likelihood estimation,
Hypothesis testing and goodness of fit

Credits 3
Pre-requisite AST-303, AST-304

AST- 408
Description

Introduction to Life insurance: life insurance and annuity contracts, pension benefits, mutual and proprietary insurers
Survival Models: Actuarial notation, future lifetime random variable, force of mortality, curtate future lifetime
Life tables and Selection: Life tables, fractional age assumptions, national life tables, survival models for life insurance policy holders, mortality trends
Insurance Benefits: assumptions, valuation of insurance benefits
Annuities: Annual annuities, annuities payable continuously, increasing annuities, evaluating annuity functions
Premiums: Preliminaries, assumptions, future loss random variable, the equivalence principle
Policy Values: Policy with annual cash flows, policy with continuous cash flows, policy alterations
Multiple State Models: Alive Dead Model, Permanent disability model, the disability income insurance model, Markov multiple state models in discrete time,
Joint Life and last Survivor benefits: Joint life and last survivor benefits, a multiple state model for independent future lifetimes, a model with dependent future lifetimes, the common shock model.

Credits 3
Pre-requisite AST-201, AST-303, AST-305

AST- 409
Description

Bayesian Inference:
Bayes theorem; prior ignorance; likelihood; odds ratio; Bayes factor; Bayesian inference for discrete random variable; Bayes theorem for binomial distribution with discrete prior;
Bayesian inference for continuous random variable; Bayesian inference for normal mean; Bayesian inference for difference between means; Comparing Bayesian and frequentist inference for proportion, for mean

Decision Theory:
Fundamental concept of decision theory; action space; Bayes decision rule and related examples, Role of sufficient statistics; James-Stein estimator; Minimax rule

Robust statistics:
The meaning of robustness, deviations from parametric models and estimation theory; Inuence function (IF), gross-error sensitivity, local-shift sensitivity, rejection point, asymptotic variance, breakdown point, identification of outliers; Definitions of M-, L-, and R-estimators

Credits 3
Pre-requisite AST-303, AST-304

AST- 410
Description
• The Basics of Working with Stata: Starting a Sample Stata Session, Different Type of Files in Stata, Useful Commands in Stata, Overview of Stata Syntax
• Importing and Exporting Data in Stata: Using and Saving Stata Data Files, Inputting Raw Data, Inputting Data from Spreadsheets, Inputting Data from Other Statistical Programs, Inputting Data from Fixed-Format Text Files
• Basic Data Management in Stata: Labeling Data, Variables and Values, Creating and Recoding Variables, Subsetting Variables and Observations, Collapsing Data Across Observations, Working Across Variables, Combining Stata Data Files : Append and Merge, Reshaping Data from Wide to Long, Reshaping Data from Long to Wide
• Graphics: Introduction to Graphics, Overview of Graph Two-way Plots, Two-way Scatter plots, Combining Two-way Scatter plots, Common Graph Options
• Summary Statistics and Tables: Summary Statistics for Measurement Variables, Frequency Tables and Two-Way Cross-Tabulations, Multiple Tables and Multi-Way Cross-Tabulations, Tables of Means, Medians, and Other Summary Statistics
• ANOVA and Other Comparison Methods: One-Sample Tests, Two-Sample Tests, Analysis of Variance (ANOVA)
• Linear Regression Models: Correlation and Regression, Multiple Linear Regression, Predicted Values and Residuals, Basic Graphs for Regression, Hypothesis Tests, Dummy Variables, Automatic Categorical Variable Indicators and Interactions, Diagnostic Plots
• Models for Binary and Categorical Outcomes: Logistic Regression, Probit Regression
• Count Models: Poisson Regression, Negative Binomial Regression
• Principal Components, Factor, and Cluster Analysis: Principal Components, Factor Analysis, Cluster Analysis
• Time-series with Stata: Smoothing, Time Plot, Lag, Leads, Differences, Correlograms, Introductory Time Series Models
• Structural Equation Modeling: Introduction to SEMs, Major types of SEMs, General SEM in Stata

Credits 3
Pre-requisite AST-303, AST-304

AST- 499
Description

Each student will be required to prepare a project report and present the report in a seminar. For the project work, each student will be assigned to a teacher at the beginning of the academic year. Submission and evaluation should be made before the commencement of final examination. Fifty percent weight of the course will be allotted to project works and the remaining fifty percent for seminar presentation.
The internal members of the examination committee will evaluate the performance in the seminars and the report will be evaluated by one internal examiner and one external examiner nominated by the examination committee.

Credits 3
Pre-requisite NONE

Description

Credit-3

  • Sampling and Sampling Distributions.
  • Expectations of functions of random variables: expectation two ways, sums of random variables, product and quotient;
  • Independence of random variables, mean and variance of linear combinations of random variables
  • Deriving distributions of the linear combinations of random variables
  • Cumulative distribution function technique: distribution of minimum and maximum, distribution of sum of difference of two random variables, distribution of product and quotient;
  • Moment generating function technique: description of technique, distribution of sums of independent random variables; The transformation Y = g(X): distribution of Y = g(X), probability integral transformation;
  • Transformations: discrete random variables, continuous random variables;
  • Sampling: basic concepts of random samples, inductive inference, populations and samples, distribution of samples, statistic and sample moments; Sample mean: mean and variance
  • Central limit theorem, normal approximations to other distributions, continuity correction
  • law of large numbers, central limit theorem, Bernoulli and Poisson distribution, exponential distribution, uniform distribution, Cauchy distribution;
  • Sampling from the normal distributions: role of normal distribution in statistics, samples mean, chi-square distribution, the F-distribution, Student’s t-distribution.
  • Non-central distributions: non-central chi-squared, t, and F distributions; definitions, derivations, properties
Credits 3
Pre-requisite AST-101, AST-102

ASTA 501
Description

  • The Concept of Actuarial Science: The basics and nature of actuarial science, coverage, examples
  • The Concept of Insurance: The basics and nature of insurance – evolution and nature of insurance, functions of insurer, financial aspects of insurer operations
  • Risk Management: Provides an understanding of risk management, different types of risks, actual and consequential losses, management of risks, loss minimization techniques.
  • The Business of Insurance: Management of risk by individuals, management of risk by insurers, fixing of premiums, reinsurance and its importance for insurers, role of insurance in economic development and social security, contribution of insurance to the society.
  • The Insurance Market and Customers: The various constituents of the insurance market, Understanding insurance customers, importance of ethical behavior.
  • Insurance Terminology: Common terms used in insurance – terms common to both life and non – life insurance – terms are specific to life and non – life insurance – how insurance terms are used.
  • Life Insurance: Introduction to Life Insurance, the Actuarial Basis of Life Insurance different products offered by life insurers, term plans, pure endowment plans, combinations of plans, traditional products, linked policies, features of annuities and group policies, , Premiums and Bonuses, employee Benefits and Other business uses of Life Insurance, Group Insurance, Linked Insurance, Policy documents, premium pays, policy lapse, revival, assignment, nomination and surrender of policy, policy claims
  • General Insurance: Risks faced by the owner of assets, policy documents & forms, general insurance products, underwritings, ratings and premium, claims, reserves and accounting.
  • Health Insurance: Introduction to health insurance: basics and applications
  • Insurance Law: Development of Insurance Legislation in Bangladesh and Insurance Act 1938, Regulations of Insurance industry, the legal framework, IDRA functions and other regulatory authorities, Policy Holders Rights of Assignment, Nomination and Transfer, Protection of Policy Holders Interest, Dispute Resolution Mechanism, Financial Regulatory aspects of Solvency margin and Investments, International Trends In Insurance Regulation
  • Insurance Rules and Acts:The Insurance Rules 1958,The Insurance Act 2010,Insurance Development and Regulatory Authority Act 2010,Insurance Corporation Act 1973,Rules and Regulations made under the Insurance Act 2010.

Text Book: Jones, H. E., Long, D. L. Principles of insurance: Life, health, and annuities, 2nd edition. FLMI Insurance Education Program, Life Management Institute LOMA, 1999

Reference

  1. Vaughan, E. J., Vaughan, T. M. Fundamentals of Risk and Insurance, 10th Edition. Barnes & Noble, 1972.
  2. The Insurance Act: 1938, Legislative and Parliamentary Affairs Division, Ministry of Law, Justice and Parliamentary Affairs.
  3. Mehr, R, Cammack,E  and Rose,T. Principles of Insurance.8 Sub Edition.Irwin Series in Insurance and Economic Security, 2013.
  4. Jerry II, R. H. and Richmond, D.S. Understanding Insurance Law, 5th Edition Lexis Nexis, 2012.
Credits 3
Pre-requisite

ASTA 502
Description

  • Cash flow model of financial transactions: For a given cash flow process, determination of inflows and outflows in each future time period considering certainty and uncertainty.
  • Concepts of compound interest and discounting: Accumulation of single investment, defining present value of future payment, discounting at fixed/variable interest rate.
  • Interest or discount rates in terms of different time periods: Relationship between the rates of interest and discount over various time periods, deriving relationship between rates of interest payable once per effective period and the rate of interest payable p times per unit time period, difference between nominal and effective rates of interest.
  • Concepts of real and money interest rates: Calculating present value and accumulated value of a stream of equal or unequal payments using specified rates of interest and the net present value at a real rate of interest, calculating the present value and accumulated value of a series of equal or unequal payments made at regular intervals under the operation of specified rates of interest considering immediate and deferred payment.
  • Annuities and accumulation: Deriving formulas for annuity due, annuity payable in arrear, deferred annuity, accumulated value payable in arrear or due, perpetuity.
  • Definition of an equation of value: Defining an equation of value for certain or uncertain payments.
  • Loan scheduling: Describing flat rates and effective rates, calculating schedule of repayments under a loan and identifying interest or capital components of any repayment.
  • Discounted cash-flow techniques: Calculating net present value and accumulated profit of the receipts and payments from an investment project at given rates of interest, Calculating the internal rate of return implied by the receipts and payments from an investment project, describing and determining payback period and discounted payback period implied by the receipts and payments from an investment project, calculating money-weighted rate of return, time-weighted rate of return and linked internal rate of return on an investment or a fund.
  • Investment and risk characteristics: Describing investment and risk characteristics of fixed-interest government borrowings, fixed-interest borrowings by other bodies, index-linked government borrowings, shares and other equity type finance, derivatives.
  • Analysis of elementary compound interest problems: Calculating the present value of payments from a fixed interest security where the coupon rate is constant and the security is redeemed in one instalment, calculating upper and lower bounds for the present value of a fixed interest security that is redeemable on a single date within a given range at the option of a borrower, calculating the running yield and the redemption yield from a fixed interest security, calculating the present value or yield from an ordinary share and a property, calculating the present value or yield from an index-linked bond, calculating the price of, or yield from,  a fixed-interest security considering income tax and capital gain tax.
  • Arbitrage free pricing methods: Calculating the price of forward contracts, explaining ‘hedging’ in the case of forward contract, calculating the value of a forward contract at any time during the term of the contract in the absence of arbitrage.
  • Term structure of interest rates: Factors influencing the term structure of interest rates, explaining par yield and yield to maturity, discrete spot rates and forward rates, continuous spot rates and forward rates, defining the duration and convexity of a cashflow sequence, Redington’s theory for immunization of a portfolio of liabilities.
  • Simple stochastic models for investment returns: Describing the concept of a stochastic interest rate model and the fundamental distinction between stochastic and deterministic model.

Text Book

  1. McCutcheon, J.J. Scott W.F (2003). An Introduction to the Mathematics of Finance. Butterworth-Heineman.
  2. Sohrab Uddin M. (1992). An Introduction to Actuarial and Financial Mathematics, Bangladesh.

References

  1. Kellison S.G., (1991). The Theory of Interest. 2nd Irwin.
  2. Garrett, S. J. (2013). An Introduction to the Mathematics of Finance: A Deterministic Approach. 2nd Butterworth-Heinemann.
  3. Newton, L. Bowers, Hans, U. Gerber, James, C. Hickman, Donald, A. Jones, Cecil, J. Nesbitt (1997). Actuarial mathematics. 2nd Edition. Society of Actuaries.
Credits 3
Pre-requisite

ASTA 503
Description

  • Statistics and its origin
    Definition, uses & importance, population & sample, sources of statistical data, parameter and statistic.
  • Summarizing Data
    Data, Levels of Measurements, variable and attribute, summarizing and presenting data, frequency distribution, graphs and diagrams
  • Measures of Central Tendency
    Arithmetic mean, median, quartiles, percentiles, deciles, mode, geometric mean, and harmonic mean
  • Measures of Dispersion
    Variance, mean deviation, standard deviation, and other measures of dispersion, moments, shape characteristics of a distribution, box and whisker plots
  • Simple Linear Regression and Correlation
    Measures of correlation, rank correlation, scatter diagram, simple linear regression, assumption, least square method, properties of regression coefficient, partitioning the total variation in regression, coefficient of multiple determination
  • Probability
    Meaning, definition, scope, set theory, sample space, elements of set theory; axiomatic definition of probability, permutation and combination, conditional probability and rules of probability for dependent and independence cases, and Bayes theorem;
  • Probability function and mathematical expectation
    Random variables, probability density function, distribution function; joint marginal and conditional distributions; mathematical expectation, expectations of sums and products of random variables; variance, conditional expectation and variance.
  • Discrete Probability Distributions
    Bernoulli, binomial, Poisson, geometric, negative binomial, hypergeometric, and uniform distributions
  • Continuous Probability Distributions
    Uniform, exponential, gamma, beta, normal, log- normal, and Weibull distributions
  • Generating Functions
    Identification of Moment and Cumulant generating functions, characteristic function of discrete and continuous distributions; determination of probability generating function of discrete and integer-valued random variables
  • Sampling Distribution
    Basic concepts of random samples, sampling and sampling distribution, expectations of functions of random variables: sums of random variables, product and quotient; independence of random variables, mean and variance of linear combinations of random variables
  • Distributions of the linear combinations of random variables: cumulative distribution function technique, moment generating function technique, transformations technique
  • Law of large numbers, central limit theorem, standard normal distribution, chi-square distribution, F-distribution, t-distribution,
  • Cauchy-Schwartz, Markov and Chebyshev’s inequality

Text Book

  1. Rohatgi V.K. and Saleh A.K.M. (2000). An Introduction to Probability and Statistics. 2nd Edition. A Wiley-Interscience Publication.
  2. Mostafa M.G. (1989). Methods of Statistics. Dhaka: Karim Press & Publication.

References:

  1. Daniel W. (2009). Biostatistics: Basic Concepts and Methodology for the Health Science. 9th WSE.
  2. Bulmer M .G. (1967). Principles of Statistics. 2nd Oliver and Boyd, Edinburgh.
  3. Ross S. (2012). A First course in Probability. 9th Pearson Prentice Hall, NJ.
  4. Mood A.M., Graybill F.A. and Boes D.C. (1974). Introduction to the Theory of Statistics. 3rd McGraw-Hill.
  5. Meyer P.L. (1970). Introductory Probability and Statistical Applications. Addison-Wesley, USA.
  6. Islam, M.N. (2004). An Introduction to Statistics and Probability. 3rd Mullick Brothers.
  7. Roy, M.K. (2001). Fundamentals of Probability and Probability Distributions. 3rd Romax Publications.
  8. Ross S.M (1988). A First course in Probability. 3rd edition. Macmillan.

 

Credits 3
Pre-requisite

ASTA 504
Description

  • Methods of finding estimators: methods of moments, maximum likelihood, and other methods
  • Properties of point estimators: closeness, mean-squared error, loss and risk functions
  • Sufficiency: sufficient statistics, factorization criterion, minimal sufficient statistics, ancillary statistics
  • Completeness: complete statistics, exponential family
  • Parameter Estimation: point estimates of mean, proportion, and variance. Confidence intervals for parameters: mean, proportion, and variance. Large sample properties and procedures
  • Test of hypothesis: simple hypothesis & composite hypothesis, critical region, best critical region, Neyman-Pearson fundamental lemma, most powerful tests, uniformly most powerful critical region, UMP tests. Hypothesis testes for mean, proportion, and variance
  • NonParametric Tests: Goodness-of-fit tests (Kolmogorov-Smirnov two-sample test for general differences, Run test) , Sign test and associated interval and point estimates for one-sample data, Signed rank test, interval and point estimates for one-sample data, Wilcoxon signed rank test, Wilcoxon sum rank test, Mann-Whitney U test, Kruskal-Wallis test, Asymptotic relative efficiency comparisons, Rank sum test, interval and point estimates for two-sample data, Two-Way Layout: tests and multiple comparison procedures, Kendall’s tau procedures for independence of two random variables
  • Bayesian Inference: Bayes theorem; prior ignorance; likelihood ratio; Bayes factor; Bayesian inference for discrete random variable; Bayes theorem for binomial distribution with discrete prior; Bayesian inference for continuous random variable; Bayesian inference for normal mean; Bayesian inference for difference between means; Comparing Bayesian and frequentist inference for proportion and mean, Loss function, Risk functions, related problems
  • Design of Experiments
    Complete Randomize Design (CRD), Randomized Block Design (RBD), Latin Squares Design (LSD), estimating model parameters; example of real life application of these experiments; comparisons among treatment means, contrasts, orthogonal contrasts, Scheffe’s method, comparing pairs of treatment means, The two-factor factorial design; statistical analysis of fixed effects, random effects, and mixed effects models; Analysis of Covariance; Description of the procedure; Factorial experiments with covariates.

Text Book

  1. Casella, G. and Berger, R.L.O. (2002). Statistical Inference. 2nd Edition. Duxbury, New York.
  2. Montogomery, D.C. (2001). Design and Analysis of Experiments. 5th John Wiley and Sons Inc.

References

  1. Johnson, N.L, Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions. Vol. 1.  2nd Edition. John Wiley, New York.
  1. Hogg, RV and Craig, AT (2012). Introduction to Mathematical Statistics. 7th Pearson.
  2. Mood, A.M., Graybill, F.A. and Boes. D.C. (1974). Introduction to the Theory of Statistics. 3rd McGraw-Hill.
  3. Kvam, P.H. and Vidakovic B. (2007). Nonparametric Statistics with Applications to Science and Engineering.
  4. Sprent, P. and Smeeton, N.C. (2001). Applied Nonparametric Statistical Methods.3rd Chapman & Hall/CRC.
  1. Kendall, M., Stuart, A. and Ord, J.K. (1998). Kendall’s Advanced Theory of Statistics, Distribution Theory. Vol 1. 6th Edition. Oxford University Press, USA.
  2. Kendall, M., Stuart, A. and Ord, J.K. (1999). Kendall’s Advanced Theory of Statistics, Classical Inference and the Linear Model. Vol 2A. 6th Edition. Oxford University Press, USA.
  3. O’ Hagan A. (1994). Kendall’s Advanced Theory of Statistics, Vol 2B: Bayesian Inference. Edward Arnold.
  4. Cox, D.R. & Hinkley, D.V. (1974). Theoretical Statistics. 2nd Edition. Chapman and Hall, London.
  5. Hoel, P.G. (1984). Introduction to Mathematical Statistics. 5th Ed. Wiley, NY.
  1. Bolstad, W.M. (2007). Introduction to Bayesian Statistics.2nd Wiley.
  2. Lee, P .M. (2004). Bayesian Statistics: An Introduction.3rd Wiley.
  3. Kirk,R.E. (2012): Experimental Design. 4th Edition. SAGE Publications, Inc.

 

Credits 3
Pre-requisite

ASTA 505
Description

  • Simple Linear Regression Model
    Least squares estimation, estimation of variance, inferences, interval estimation, prediction, Analysis of Variance, R-square, residual analyses, transformations as solution to problems with the model
  • Multiple Regression Models
    Basic estimation and inference for multiple regression, Generalized Least Squares and Weighted Least Squares, Extra Sum of Squares Principles and related tests; multicolliniarity, autocorrelation, model diagnostics and selecting the best regression equations
  • Generalized linear models: exponential family of distributions; Properties of distributions in Exponential family, Component of GLM, Random systematic link function; method of maximum likelihood, method of least squares estimation of generalized linear models; Scores and information matrices; confidence intervals for model parameters, adequacy of a model, log-likelihood ratio statistic (deviance), assessing goodness of fit, hypothesis testing
  • Models for binary responses: generalized linear models,  general logistic regression, maximum likelihood estimation and log-likelihood ratio statistic, other criteria for goodness of fit, least square methods; multinomial distributions; ordinal logistic regression models
  • Models for count Data: log-linear models, maximum likelihood estimation, hypothesis testing and goodness of fit

Reference 

  1. Draper, N.R. and Smith, H. (1999). Applied regression analysis. 3rd Wiley.
  2. Kutner, M., Nachtsheim, C. and Neter, J. (2004). Applied Linear Regression Models. 4th McGraw Hill/Irwin Series.
  3. Chatterjee, S. and Hadi, A.S. (2012). Regression Analysis by Example. John Wiley, NY.
  4. Graybill, F.A. (1961). An Introduction to Linear Statistical Models. Vol-1. McGraw Hill, NY.
  5. Montogomery, D.C, Peck, E. and Vining, G.G. (2007). An Introduction to Linear Regression Analysis. 4th Edition. John Wiley, NY.

 

Credits 3
Pre-requisite

ASTA 506
Description

  • Investment and asset management: Principal terms in use
  • Key principles of finance: Relationship between finance, real resources, and objectives of an organization, relationship between the stakeholders in an organization (including lenders and investors), the role and effects of the capital markets, agency theory, the theory of the maximization of shareholder wealth
  • Forms of Business Organization: Characteristics of sole traders, partnerships and limited companies as business entities, different types of loan and share capital, public and private company, and limited company
  • Company finance: Medium Term Company Finance, hire purchase, credit sale, leasing, bank loans, Short term Company Finance: bank overdrafts, trade credit, factoring, bills of exchange, commercial paper
  • Principles of personal and corporate taxation: Basic principles of personal taxation, basic principles of the taxation of capital gains, basic principles of company taxation, different systems of company taxation from the points of view of an individual shareholder and the company, basic principles of double taxation relief
  • Principal forms of financial instrument: Methods for seeking a quotation on stock exchange and seeking a quotation for securities debenture stocks, unsecured loan stocks, Eurobonds, preference shares, ordinary shares, convertible unsecured loan stocks, convertible preference shares, warrants, floating rate notes, subordinated debt, options issued by companies, issues of securities, scrip issue, rights issue, financial futures, options, interest rates, currency swaps
  • Capital Structure and Dividend policy: Capital structure, financing and valuation, market valuation, dividend policy, distribution of profits
  • Capital Budgeting and Risk Management: Introduction to Risk and Return, Portfolio Theory and the Capital Asset, Pricing Model, Risk and the Cost of Capital, Managing Risk, Project Analysis, Investment, Strategy, and Economic Rents, Agency Problems, Compensation, and Performance Measurement, Working Capital Management
  • Financial institutions: Central banks, investment exchanges, investment banks, clearing banks, building societies, investment trusts, unit trusts, investment management companies, self-administered pension funds, life insurance companies, general insurance companies
  • Role and Principal Features of Accounts of a Company: Introduction to financial statements, key accounting treatments, Introduction to management accounting and relevant costs for decisions, Costing, Budgeting and budgetary control, interpretation of reports and company accounts, contents and features of insurance company accounts
  • Insurance Rules 1958, Insurance Rules and Regulations made under the Insurance Act 2010 and Insurance Development and Regulatory Authority Act 2010

References:

  1. Atrill, P., McLaney, E. Accounting and finance for non-specialists. 9th ed. Prentice Hall, 2015.
  2. Brigham, E. F., Houston, J. F. Fundamentals of financial management (concise edition). 7th ed. South-Western, 2011.
  3. Davidson, A. How to understand the financial pages. 2nd ed. Kogan Page, 2008.
  4. Holmes, G., Sugden, A., Gee, P. Interpreting company reports and accounts. 10th ed. Prentice Hall, 2008
  5. Brealey, R. A., Myers, S. C., Allen, F Principles of corporate finance (Global edition). 11th ed. McGraw-Hill, 2014.
Credits 3
Pre-requisite

ASTA 507
Description

  • Introduction: Basic concept of demography; sources of demographic data: census, vital registration system, sample surveys, and population register types of errors and methods of testing the accuracy of demographic data.
  • Population growth: Components, techniques to measure it, doubling time, population estimates and projections, different techniques of population projection-component method, arithmetic/linear method, geometric method, exponential method etc. need of population projections. Gompartz & Makehaum curves, Logistic curve
  • Fertility and Mortality: measures of fertility, crude birth rate, age specific fertility rates, general fertility rate, total fertility rate, gross reproduction rate and net reproduction rate; measures of mortality; crude death rate, age specific death rates, infant mortality rate, child mortality rate, neo-natal mortality rate, standardized death rate its need and use, sex ratio, dependency ratio, density of population.
  • Life Table: Concept, structure and calculation; complete and abridged life table, different life table functions and inter-relationships among them, use of life table, Actuarial life table, competing risk life table, multiple decrement life table.
  • Force of Mortality: Idea and definition calculation of life table with the help of force of mortality, stable and stationary population, their characteristics and uses, Lotka’s characteristics equation, intrinsic birth and death rates
  • Parametric Regression Models: Inference procedure for exponential distribution, for gamma distribution, models with polynomial based hazard function, interval censored or truncated data, log-location scale regression model, proportional hazard regression model, graphical methods for model selection, inference for log-location scale models, and extension of log-location scale models
  • Nonparametric & Graphical Procedures: Nonparametric estimation of a survivor function and quintiles, actuarial and Kaplan-Meier methods, Nelson-Aalen estimate, plots involving survivor or cumulative hazard function, estimation of hazard or density function, methods for truncated and interval censored data
  • Censoring & Likelihood: Types of censoring and maximum likelihood, truncation
  • Survival Analysis: Basic concepts, lifetime distribution, continuous model, discrete model, hazard function, exponential distribution, Weibull distribution, log-normal distribution, log-logistic distribution, gamma distribution, regression models
  • Semi-parametric hazards regression model: estimation of parameters, inclusion of strata, time-dependent covariates, residuals and model checking, methods for grouped or discrete lifetimes, related topics on the Cox model, rank tests for comparing distributions, estimation for semi-parametric accelerated failure time models
  • Multiple Models of Failure: Basic characteristics of model specification, likelihood functions formulation, nonparametric methods, parametric methods, semi-parametric methods for multiplicative hazards model
  • Analysis of Correlated Lifetime Data: regression models for correlated lifetime data, representation and estimation of bivariate survivor function.

Demography

  1. Shryock, H.S. and Siegel, J.S. and Larmon, A.E. (1975). The Methods and Materials of Demography. Vol-1 & 2. U.S. Department of Commerce Publication
  1. Lawless, J.F. (2003). Statistical Models and Methods for Lifetime Data. 2nd Edition. Wiley.

References

  1. Siegel, S.J. and Swanson, D.A. (2004). The Methods and Materials of Demography. 2nd Edition. Elsevier
  2. Spiegelman (1968). Introduction to Demography. Revised Edition. Harvard University Press, Cambridge
  3. Kpdekpo, G.M.K. (1982). Essentials of Demographic Analysis for Africa. Heinemann International Literature & Textbooks
  4. Kalbfleisch, J.D. and Ross, L.P. (2002). The Statistical Analysis of Failure Time Data. 2nd Edition. Wiley.
  5. Anderson J.A., Dow J.B., Actuarial Statistics VOL II Construction of Mortality and Other Tables. Cambridge University Press. Published for the Institute and Faculty of Actuaries
  6. Klein J.P., Moeschberger M.L. (2003) Survival Analysis: Techniques for Censored and truncated data. 2nd edition. Springer Verlag.
Credits 3
Pre-requisite

ASTA 508
Description

  • Introduction to Life insurance: life insurance and annuity contracts, pension benefits, mutual and proprietary insurers
  • Probability concepts: joint, marginal, and conditional probability
  • Survival Models: Actuarial notation, future lifetime random variable, force of mortality, curtate future lifetime random variable.
  • Life tables and Selection: Life tables, different life table functions and inter-relationships among them, cause specific competing risk life tables, multiple decrement life table, fractional age assumptions, national life tables, Actuarial life table, survival models for life insurance policy holders, mortality trends
  • Insurance Benefits: assumptions, valuation of insurance benefits
  • Annuities: Annual annuities, annuities payable continuously, increasing annuities, evaluating annuity functions
  • Premiums: Preliminaries, assumptions, future loss random variable, the equivalence principle
  • Policy Values: Policy with annual cash flows, policy with continuous cash flows, policy alterations
  • Multiple State Models: Alive Dead Model, Permanent disability model, the disability income insurance model, Markov multiple state models in discrete time,
  • Joint Life and Last Survivor Benefits:  Joint life and last survivor benefits, a multiple state model for independent future lifetimes, a model with dependent future lifetimes, the common shock model.
  • Pension Mathematics: Summary, Salary Scale Function, Valuation of Benefits, Service table
  • Yield curves and Non-diversifiable Risk: Yield Curve, valuation of Insurances and Life annuities, Diversifiable and non-diversifiable Risk, Monte Carlo Simulation
  • Emerging Costs for Traditional Life Insurance: Introduction, profit testing a term insurance policy, Profit testing Principles, Profit measures, Profit testing Multiple State Models
  • Simulation: The Inverse Transform method, The Box Muller method, The Polar method

Text Book:

  1. Dickson, D.C.M., Hardy, M.R. and Waters, H.R. (2013). Actuarial mathematics for life contingent risks. 2nd Edition. Cambridge University Press

References

  1. Benjamin, B. and Pollard, J.H. (1993). The Analysis of Mortality and other Actuarial Statistics. 3rd Edition. Institute and Faculty of Actuaries
  2. Jordan, C.W. (1975). Life Contingencies. 2nd Edition. Chicago: Society of Actuaries
  3. Moller T., and Steffensen M. (2007) Market Valuation Method in Life and Pension Insurance. Cambridge University Press
  4. Hooker P.F. and Logley-Cook L.H. Life and Other Contingencies VOL I. Cambridge University Press. Published for the Institute and Faculty of Actuaries.
  5. Newton L. Bpwers, hans, U.gerber, Jame, C. Hickman, Donald, A. Jones, Cecil, J. Nesbitt (1997). Actuarial Mathematics. 2nd edition. Society of Actuaries.
  6. Sohrab Uddin M. (1992) An Intruduction to Actuarial and Financial Mathematics
Credits 3
Pre-requisite

ASTA 509
Description

  • Risk environment: Risk management process, the design of products, schemes, contracts and other arrangements, risk classification, systematic and diversifiable risk, risk appetite and risk efficiency, credit risk and credit ratings, liquidity risk, market risk, operational risk, business risk, attitudes to and methods of risk acceptance, rejection, transfer and management for stakeholders
  • Regulatory environment: the regulatory regimes, the concept of information asymmetry, fairness of financial contracts, implications of a requirement to treat the customer fairly
  • External environment: implications of: legislation – regulations, State benefits, tax, accounting standards, capital adequacy and solvency, corporate governance, risk management requirements, competitive advantage, demographic changes, environmental issues, international practice
  • Investment environment: the cash-flows of simple financial arrangements and the need to invest appropriately to provide for financial benefits on contingent events, the principal economic influences on investment markets, relationships between the total returns and the components of total returns, on equities, bonds and cash, and price and earnings inflation.
  • Capital requirements: the main providers of benefits on contingent events need capital, the implications of the regulatory environment, measures of capital needs, economic balance sheet, in order to consider the capital requirements of a provider of benefits on contingent events
  • Contract design: the factors to be considered in determining a suitable design for financial structures e.g. products, schemes, contracts or other arrangements
  • Project planning and management: the process of project management, actuarial techniques of capital investment projects and cost-benefit analyses
  • Data: the data requirements for determining values for assets, future benefits and future funding requirements, the ideal data, the appropriate grouping of data
  • Risk management: the issues surrounding the management of risk, tools and methods of measuring risk, risks with low likelihood but high impact, the use of scenario analysis, stress testing and stochastic modelling in the evaluation of risk
  • Modelling: the use of actuarial models, requirements for building a model, project future cash and revenue flows, the use of these models for– pricing or setting future financing strategies – risk management – assessing the capital requirements – pricing and valuing options and guarantees, sensitivity analysis of the results of the models; Assumption setting; Expenses; Developing the cost and the price; Investment management; Provisioning; Relationship between assets and liabilities
  • The solution: Maintaining profitability, Determining the expected results; Reporting actual results; Asset management; Capital management; Surplus management; Insolvency and closure; options and guarantees;
  • Monitoring: the actual experience can be monitored and assessed in terms of: monitoring experience, the data required, the various factors affecting the experience, revised models and assumptions.

Text Book

  1. Allen, S.L., Financial Risk Management: A Practitioner’s Guide to Managing Market and Credit Risk, 2nd Edition, Wiley.

References:

  1. Denuit,M.; Dhaene,J.; Goovaerts,M.; Kaas,R.,(2005), Actuarial Theory for Dependent Risks: Measures, Orders and Models, Wiley
  2. Brown,A., Financial Risk Management For Dummies, 3rd edition, Wiley.
  3. Hardy,M.,(2003), Investment Guarantees: Modeling and Risk Management for Equity-Linked Life, Wiley
  4. Poitras,G., Risk Management, Speculation, and Derivative Securities, 1st Academic Press.
  5. Sweeting,P., Financial Enterprise Risk Management,  1st edition, Cambridge University Press.
Credits 3
Pre-requisite

ASTA 510
Description

Statistical analysis using R, SPSS or SAS for the following topics-

Linear regression analysis: parameter estimates, ANOVA, and tests of significance

Non-linear regression analysis: parameter estimates, confidence intervals and hypothesis tests; One factor and two factor factorial experiments and tests; Large data management

Multivariate analysis: Principal component analysis; Factor analysis; Cluster analysis; Profile analysis; other multivariate analysis

Generalized Linear Model, general logistic regression, maximum likelihood estimation and log-likelihood ratio statistic and Generalized Estimating Equation, Cox PH model

Text Book: Everitt, B. and Hothorn, T. (2006). A Handbook of Statistical Analyses Using R.
Chapman & Hall/CRC, Boca Raton, FL. ISBN 1-584-88539-4

Reference

  1. Dalgaard, P. (2008). Introductory Statistics with R. Springer, 2nd Edition, ISBN 978-0387-79053-4
  2. Der, G. and Everitt, B.S. A Handbook of Statistical Analysis Using SAS. 3rd Edition. CRC Press
Credits 3
Pre-requisite

ASTA 511
Description

  • Modern probability: probability as a set function; Borel field and extension of probability measure; probability measure notion of random variables; probability space; distribution function; expectations and moments, convergence of random variables, Laplace transformation
  • Stochastic Process: Introduction, distinction between deterministic and stochastic models, Random Walk, concept and properties of discrete random walks and random walks with normally distributed increments, both with and without drift
  • Markov Chain: introduction, transition probability matrices of a Markov chain, first step analysis, some special Markov chains, regular transition probability matrices, classification of states; basic limit theorem of Markov chain; reducible Markov chains;
  • Poisson process: counting and Poisson process; the law of rare events
  • Continuous time Markov chain: pure birth processes; pure death processes; birth and death processes; limiting behavior of birth and death processes; birth and death process with absorbing states; finite state continuous time Markov chains
  • Renewal theory and its applications: introduction, distribution of N(t), limit theorems and their applications, renewal reward process regenerative process, semi-Markov process
  • Queuing Process
    • the connection between Poisson process and the Poisson distribution, Poisson process as
    • the distribution of waiting between events
    • the distribution of process increments
    • the behavior of the process over an infinitesimal time interval
  • Compound Processes: Compound Binomial, Compound Poisson, Compound Negative Binomial Random variables

Text Book

  1. Taylor, H.M. and Karlin, S. (1998). An Introduction to Stochastic Modeling. 3rd Edition. Academic Press

References:

  1. Ross, S. (2003). Introduction to Probability Models. 8th Edition. Elsevier
  2. Grimmett, G. and Stirzaker, D. (2001). Probability and Random Processes. 3rd Edition. Oxford University Press, USA.
  3. Karlin S. and Taylor H.M. (1975). A First Course in Stochastic Processes. 2nd Edition.  Academic Press. ISBN 0-12-398552-8
  4. Bailey, N.T.J. (1964). The Elements of Stochastic Processes with Applications to the Natural Sciences. John Wiley
  5. Bartlett, M.S. (1978). An Introduction to Stochastic Processes. 3rd Edition. Cambridge University Press. Wiley, NY
  6. Grandell J. (1997). Mixed Poisson Process. Chapman and Hall
  7. Kijima M. (2000). Stochastic Processes with applications to Finance. Chapman and Hall

 

 

Credits 3
Pre-requisite

ASTA 512
Description

  • Basic concepts and introduction: utility function and utility theory, the economic properties of commonly used utility functions, dependent utility functions, utility maximization, economic characteristics of consumers and investors: non-satiation risk aversion, risk neutrality and risk seeking ,declining or increasing absolute and relative risk aversion, the traditional theory of consumer choice, utility functions to compare investment opportunities, for first and second-order dominance, behavioral finance.
  • Investment risk: measures of investment risk: variance of return, downside semi-variance of return, shortfall probabilities, Value at Risk (VaR) / Tail VaR, investor’s utility function, investment opportunities, distribution of returns, thickness of tails, assessment of risk.
  • Mean-variance portfolio theory: assumptions of mean-variance portfolio theory, application of mean-variance portfolio, optimum portfolio, diversification using mean-variance portfolio theory.
  • Single and multifactor models: multifactor models: macroeconomic models, fundamental factor models, statistical factor models, single index model, diversifiable and non-diversifiable risk, construction of multifactor models.
  • The principal results, assumptions and limitations: Sharpe-Lintner-Mossin Capital Asset Pricing Model (CAPM), the theory to overcome these limitations, the Ross Arbitrage Pricing Theory model (APT)
  • Efficient Markets hypothesis: Efficient Markets Hypothesis for investment management, the evidence for or against each form of the Efficient Markets Hypothesis.
  • Stochastic models of the behavior of security prices: security prices and the empirical evidence, auto-regressive models, Wilkie model, data availability, data errors, outliers, stationarity of underlying time series, the role of economic judgment.
  • Brownian motion (or Wiener Processes): standard Brownian motion, stochastic differential equations, the Ito integral, diffusion, mean-reverting processes, Ito’s formula, the stochastic differential equation for geometric Brownian motion, equation for the Ornstein-Uhlenbeck process.
  • Option prices, valuation, hedging: arbitrage and a complete market, option prices, forward contract, call and put options, put-call parity, binomial trees and lattices in valuing options, binomial lattice, the pricing of equity options, the real-world measure, the risk-neutral measure, the risk-neutral, state-price deflator approaches, the Black-Scholes derivative-pricing model: a complete market, risk-neutral pricing, the equivalent martingale measure, the Black-Scholes partial differential equation, price and hedge, the Black-Scholes model, binomial model, the Black-Scholes model, the risk-neutral pricing approach, the commonly used terminology, partial derivatives (the Greeks) of an option price.
  • Interest rates: the term-structure of interest rates, the pricing of zero coupon bonds, interest-rate derivatives, one-factor diffusion model, the risk-free rate of interest, state-price deflators, zero-coupon bonds and interest-rate derivatives, the Vasicek, Cox-Ingersoll-Ross and Hull-White models, one-factor models, simple models for credit risk, the terms credit event, recovery rate, structural models, reduced form models, intensity-based models, the Merton model, two-state model, constant transition intensity, the Jarrow-Lando-Turnbull model, the two-state model, stochastic transition intensity.

Text Book

  1. Panjer, H. H 2001, Financial economics: with applications to investments, insurance and pensions. The Actuarial Foundation.

Reference

  1. Baxter M., Rennie A. 1996. Financial calculus: an introduction to derivative pricing. CUP.
  2. Cairns, Andrew J. G. 2004 Interest rate models: an introduction. Princeton University Press.
  3. Joshi, MS. Paterson, JM. 2013 Introduction to mathematical portfolio theory. Cambridge University Press.
  4. Elton EJ, Gruber, MJ, Brown, SJ. et al. 2014 Modern portfolio theory and investment analysis. 9th ed. John Wiley.
  5. Karatzas I., Sharve S.E. (1998) Methods of Mathematical Finance. Spring Verlag
  6. Musiela M., Rutkowska M. (2007). Martingale Methods in Financial Modeling. 2nd Edition. Spring Verlag

 

Credits 3
Pre-requisite

ASTA 513
Description

  • Basic econometric models, assumptions, and parameter estimation
  • Multicollinearity: nature, detection, consequence and remedy of multicollinearity
  • Autocorrelation: definition, detection, consequence and remedy
  • Heteroscedasticity: definition, detection, consequence and remedy
  • Model Specification: Consequences of under and over specification, model selection criteria
  • Estimation and application of Cobb-Douglas production function
  • Simultaneous equation models:
    • Simultanious equation bias
    • Inconsistance of OLS estimations
    • Types and rules of identification
    • Estimation of simultanious estimation methods: Methods of indirect least- square (ILS) and two stage least square (2 SLS)
  • Non-Linear regression:  
    • Least Square Estimation,
    • Estimating the Parameter: Response surface methodology, Semilogarithm
    • Time series Econometrics: Stationarity, Unit roots and co-integration, Spurious regression, Dynamic Econometrics model, Distributed lag models.
  • Panel Data Models: 
    • Fixed Effects
    • Random Effects
    • Dynamic Model
  • Introduction to Time Series: examples of time series, objectives, types of variation, stationarity, trends and seasonal components, no seasonal component, time plot
  • Autocovariance of a Stationary Time Series: Stationarity, applied to stationary time series, drawbacks of shift operator, backwards difference, the spectral density, time series models, Box-Jenkins model, concept of a filter, root characteristic equation of time series, estimation of the mean and the autocovariance, Multivariate Autoregressive model;

AR process, MA process, ARMA processes, calculation of the ACVF, Prediction of an ARMA Process, cointegrated time series, ARIMA time series

  • Forecasting: Introduction, univariate procedures, multivariate procedures, comparative review of forecasting procedures, prediction theory

Text Book

  1. Gujarati, Damodar N. Basic Econometrics. New York: McGraw-Hill, Fifth Edition.
  2. H. Greene (2011). Econometric Analysis. 7th Edition. Prentice Hall.

References:

  1. M. Wooldridge (2010). Econometric Analysis of Cross Section and Panel Data. 2nd Edition. The MIP Press.
  2. M Verbeek (2000). A guide to Modern Econometrics. 3rd Edition, John Wiley & Sons
  3. Makridakis S., Wheelwright C., and Hyndman R. J. (1997) Forecasting Methods and Applications, 3rd Edition, Wiley.
  4. Chatfield, C. (2003). The Analysis of Time Series. 6th Edition, Chapman Hall.

 

Credits 3
Pre-requisite

ASTA 514
Description

  • Legislative and regulatory framework for investment: knowledge of the legislative and regulatory framework for investment management and the securities industry in Bangladesh
  • The framework of regulation of investment industry: the relevant professional guidance for actuaries working in the investment field, The Insurance Act 2010, Insurance Act 1938, Insurance Development and Regulatory Authority Act 2010, Insurance Corporation Act 1973, Rules and Regulations made under the Insurance Act 2010, the circumstances in which actuaries require authorization under the Financial Services and Markets Acts,
  • The taxation treatment: The taxation treatment of different forms of investment for individual and institutional investors
  • The principles and objectives of investment management and analyses: Analyses the particular liability characteristics, investment requirements and the influence of the regulatory environment on the investment policies, life insurance company policies, general insurance company, health and care insurance company, self-administered defined benefit pension fund, self-administered defined contribution pension fund, pure fund manager,  the investment vehicles into account taxation, expenses and other relevant considerations
  • The investment indices and global investors
  • The principal techniques in portfolio management including risk control techniques; the principal active management “styles” (value, growth, momentum, rotational), passive fund management, investment management assessment and selection, investment management of a large portfolio, structure of an institutional investment department, performance measurement service
  • The principal investment assets and the markets: the processes of dealing, transfer and settlement processes in the main equity, bond and derivative markets, the processes of dealing, transfer and settlement processes in the main overseas equity, bond and derivative markets, levels of charges, expenses and dealing spreads for an institutional investor, main features of the capital markets in the developed and emerging markets.
  • Specialist investment assets and the markets: asset-backed securities, unquoted equities, including venture capital (“private equity”) investment, property finance and development, Analyses more complex problems in terms of actuarial, economic and financial factors to a level where appropriate analytical techniques, and interpret the results in a wider context and draw appropriate conclusions.

 Text Book

  1. Bodie, Z., Kane, A., Marcus, A. J. (2011). 9th ed. McGraw-Hill.

References:

  1. Chandra, P. Investment Analysis and Portfolio Management. Fourth Edition. Tata McGraw Hill.
  2. Tavakoli, J.M. (2001). Credit derivatives and synthetic structures: a guide to instruments and applications. 2nd Wiley.
  3. Clark, G. (2007). A Farewell to Alms: a brief economic history of the world. Princeton University Press.
  4. Saunders, A. (2011), Foreign exchange risk [in: Financial institutions management: a modern perspective]. 7th ed. McGraw-Hill.
  5. Hull, J. C. Options, futures and other derivatives. 8th ed. Pearson.

 

Credits 3
Pre-requisite

AST-101
Description

Statistics and its origin:
Defining Statistics, Characteristics of Statistics, Uses & Importance of Statistics, Population & Sample; sources of Statistical Data, Parameter and Statistic.

Summarizing Data:
Meaning of Data, Level of Measurement, Variable and attribute, Summarizing and Presenting Data, Frequency Distribution, Formation of Discrete and Continuous Frequency Distribution, Cumulative Frequency Distribution, Presenting Data by Graphs and Diagrams, Presentation of Qualitative Data, Presentation of Quantitative Data.

Descriptive Statistics I: Measures of Central Tendency
Measures of central tendency, arithmetic mean, median, quartiles, percentiles and deciles, mode, geometric mean, harmonic mean, other measures of average, comparing the averages, properties of measures, effects of change in origin and scale, stem and leaf plot

Descriptive Statistics II: Measures of Dispersion
Meaning of dispersion, measures of dispersion, absolute measures of dispersion, relative measures of dispersion, empirical relations among measures of dispersion, comparing the measures, moments, central moments in terms of raw moments, effects of change in origin and scale on moments, Sheppard’s correction for moments, shape characteristics of a distribution, box and whisker plots.

Simple Linear Regression and Correlation:
Correlation analysis, measuring the correlation, rank correlation, regression analysis, simple linear regression model, scatter diagram, leAST- square method, properties of regression coefficient, partitioning of the total variation in regression, Coefficient of multiple determination

References:

  1. Mostafa, M.G. (1989). Methods of Statistics. Dhaka : Karim Press & Publication
  2. Daniel, W. (2009). Biostatistics: Basic Concepts and Methodology for the Health Science. 9th Edition. WSE
  3. Hoel, P. G. (1984). Introduction to Mathematical Statistics.5th Edition. John Wiley, NY
  4. Wonnacott, T.H. & Wonnacott, R.J. (1990). Introductory Statistics. 5th Edition. John Wiley, NY
  5. Yule, G.U. and Kendall, M.G. (1968). An Introduction to the Theory of Statistics. 14th Edition. Charles-Griffin, London
  6. Islam, M.N. (2004). An Introduction to Statistics and Probability. 3rd Edition. Mullick Brothers.

 

Credits 3
Pre-requisite

AST-102
Description

  • Meaning of probability; definition and scope of probability;
  • Set theory; sample space; elements of set theory; axiomatic definition of probability;
  • permutation and combinations;
  • conditional probability and rules of probability for dependent and independence cases;
  • Bayes theorem;
  • Random variables; probability function and probability density function;
  • Distribution function; joint probability function; marginal and conditional distributions.
  • Mathematical expectations; expectations of sums and products of random variables; variance
  • Conditional expectation and variance; Cauchy-Schwartz, Markov and Chebysheb inequality
  • Evaluation of probabilities (by calculation or by referring to tables as appropriate with the distributions.
  • Moment and cumulant generating functions; characteristic function; probability generating function; (definitions and only for discrete distributions)

References:

  1. Ross, S. (2012). A First course in Probability. 9th Pearson Prentice Hall, NJ
  2. Rohatgi, V.K. and Saleh, A.K.M. (2000). An Introduction to Probability and Statistics. 2nd A Wiley-Interscience Publication
  3. Meyer P.L. (1970). Introductory Probability and Statistical Applications. Addison-Wesley, USA
  4. Mosteller F., Rourke E.K.R. and Thomas G.B. (1970). Probability with Statistical Applications. 2nd Edition. Addison-Wesley, USA

 

Credits 3
Pre-requisite

AST-201
Description

  • Random variables; probability mass function, cumulative density function and probability density function
  • Discrete Probability Distributions: Bernoulli, binomial, Poisson, geometric, negative binomial, Hypergeometric, uniform
  • Continuous Probability Distributions: uniform, exponential, gamma, beta, normal, log- normal, Weibull
  • Identification of Moment and cumulant generating functions; characteristic function of discrete and continuous distributions
  • Showing moments from Moment and cumulant generating functions; characteristic function
  • Distribution of a function of a random variable from the distribution of a random variable
  • Determination of probability generating function of discrete and integer-valued random variables
  • Application of PGF, MGF, CGF and cumulants and the reason of their use
  • Joint, Marginal and conditional distributions
  • Law of large numbers; and central limit theorem.
  • Cauchy-Schwartz, Markov and Chebysheb inequality

References:

  1. Ross, S. (2012). A first course in Probability. 9th Edition. Pearson Prentice Hall, NJ
  2. Mood, A.M., Graybill, F.A. and Boes. D.C. (1974). Introduction to the theory of Statistics. 3rd McGraw-Hill
  3. Rohatgi, V.K. and Saleh, A.K.M. (2000). An Introduction to Probability and Statistics. 2nd Edition. A Wiley-Interscience Publication

 

Credits 3
Pre-requisite

AST-202
Description

  • Sampling and Sampling Distributions.
  • Expectations of functions of random variables: expectation two ways, sums of random variables, product and quotient;
  • Independence of random variables, mean and variance of linear combinations of random variables
  • Deriving distributions of the linear combinations of random variables
  • Cumulative distribution function technique: distribution of minimum and maximum, distribution of sum of difference of two random variables, distribution of product and quotient;
  • Moment generating function technique: description of technique, distribution of sums of independent random variables; The transformation Y = g(X): distribution of Y = g(X), probability integral transformation;
  • Transformations: discrete random variables, continuous random variables;
  • Sampling: basic concepts of random samples, inductive inference, populations and samples, distribution of samples, statistic and sample moments; Sample mean: mean and variance
  • Central limit theorem, normal approximations to other distributions, continuity correction
  • law of large numbers, central limit theorem, Bernoulli and Poisson distribution, exponential distribution, uniform distribution, Cauchy distribution;
  • Sampling from the normal distributions: role of normal distribution in statistics, samples mean, chi-square distribution, the F-distribution, Student’s t-distribution.
  • Non-central distributions: non-central chi-squared, t, and F distributions; definitions, derivations, properties

References:

  1. Ross, S. (2012). A first course in Probability.9th Edition. Pearson Prentice Hall, NJ
  2. Mood, A.M., Graybill, F.A. and Boes. D.C. (1974). Introduction to the theory of Statistics. 3rd McGraw-Hill
  3. Hogg, R.V. and Craig, A.T. (2012). Introduction to Mathematical Statistics. 7th Pearson
  4. Rohatgi, V.K. and Saleh, A.K.M. (2000). An Introduction to Probability and Statistics. 2nd A Wiley-Interscience Publication

 

Credits 3
Pre-requisite

MAT 101
Description

Differential Calculus: Functions; Basic concept of limits and continuity; Slopes and Rates of change; Techniques of differentiation, Successive differentiation, Leibnitz theorem, Indeterminate forms, Analysis of Function: Function increasing, Function decreasing, Concavity of a curve, Points of inflection, Rolle’s Theorem, Mean-Value Theorem, Taylor’s Theorem; Applications of Derivative; Maxima and minima of a function; Functions of two or more variables; Partial Derivatives, Euler’s theorem on homogeneous function.

Integral Calculus: Integration by the method of substitution, by parts. Integration of rational functions by partial fractions, Definite integrals and its properties and use in summing series. Beta function and Gamma function. Applications of definite integrals: Area under a plane curve and area of a region enclosed by two or more curves in Cartesian co-ordinate system, volumes of solids generated by revolution, volumes of hollow solids of revolution by shell method, multiple integrals with application; Jacobeans.

Text Book: Calculus: Howard Anton, Irl Bivens & Stephen Davis, 10th edition, John Wiley & Sons.

Reference      

  1. Differential Calculus: Das & Mukherjee.
  2. Integral Calculus: Das & Mukherjee.

 

Credits 3
Pre-requisite

MAT206
Description

  • Theory of Numbers: Unique factorization theorem, congruencies, Euler’s phi-function
  • Inequalities: Order properties of real numbers, Weierstrass’, Chebysev’s and Cauchy’s inequalities, inequalities involving means.
  • Complex Numbers: Field properties, geometric representation of complex numbers, operations of complex numbers.
  • Summation Series: Summation of algebraic and trigonometric finite series.
  • Theory of equations: Relation between roots and coefficients, symmetric functions of roots, Descartes rule of signs, rational roots, Newton’s method.
  • Linear Algebra: Systems of linear equations and matrices: Introduction to systems of linear equations, Gaussian elimination, Matrices and matrix operations, Inverses; rules of matrix arithmetic, Elementary matrices and a method for finding inverse of a matrix, Further results on systems of equations and invertibility, Diagonal, triangular, and symmetric matrices.
  • Determinants: Basic concept on determent, Evaluating determinants by row reduction, Properties of the determinant function, Cofactor expansion; Cramer’s rule.
  • General vector space: Real vector space, Subspace, Linear independence, Basis and dimension, Row space, column space and null space, Rank and nullity.
  • Inner product spaces: Inner products, Angle and orthogonality in inner product spaces, Orthonormal bases; Gram-Schmidt process; QR-decomposition, Best approximation; least squares, Orthogonal matrices.
  • Eigenvalues and eigenvectors: Concepts on eigenvalues and eigenvectors,
  • Linear transformation: General linear transformation, Kernel and range, Inverse linear transformations, Matrices of general linear transformations.

Text Book: (a) Higher Algebra, Md. Abdur Rahman

(b) Elementary Linear Algebra (ninth edition) – Howard Anton and Chris Rorres

(c) Theory and Problems of Complex Variables – Murray R. Spiegel

 

Reference

(a) Number Theory – S G Telang

(b) Complex Variables and Its Applications – R. V. Churchill

(c) Experiments in Computational Matrix Algebra    – David R. Hill

(d) Higher Engineering Mathematics – Grewel (36th edition)

 

Credits 3
Pre-requisite

AST- 501
Description

  • Design and implementation of Surveys with the following sampling design:
  • Simple Random Sampling, Systematic Sampling, Stratified Sampling, Cluster Sampling,
  • Questionnaire design and formatting
  • Multistage and Multiphase Sampling
  • Estimation of sample size for different sampling design in order to estimate population level point estimates and testing null hypothesis
  • Application of intra-class correlation of design effects for complete survey
  • Estimation of design weight and adjustment for non response
  • Examples of various national and international Surveys
  • Detailed discussion on Bangladesh Demographic Health Surveys (Important)

Reference: 

  1. United Nations Department of Economic and Social Affairs: Designing Household Survey Samples, United Nations, 2005
  2. Lohr S. L. (2009). Sampling Design and Analysis. Duxbury Press
  3. Levy P.S. and Lemeshow, S. (1999). Sampling of Populations: Methods and Applications, 3rd Edition, New York: Wiley Interscience
  4. Cochran, W.G. (1977).Sampling Techniques.3rd John Wiley and Sons Inc.
  5. Des Raj (1968).Sampling Theory. McGraw-Hill Inc.
Credits 3
Pre-requisite

AST – 502
Description

  1. Simple Regression Models: Review
  2. Multiple Regression Models and Estimation
  • Matrix Notation and Literacy
  • Hyper plane extension to simple linear model
  • Interaction models
  • Basic estimation and inference for multiple regression
  • Related Application

3. General Linear F test and Sequential SS

  • Reduced and Full models
  • F test for general linear hypotheses
  • Effects of a variable controlled for other predictors
  • Sequential SS
  • Partial correlation
  • Related Application

4. Multicollinearity among independent variables

  • Effect on standard deviations of coefficients
  • Problems interpreting effects of individual variables
  • Apparent conflicts between overall F test and individual variable t test
  • Benefits of designed experiments
  • Related Application
  1. Polynomial Regression Models

     6. Categorical Predictor Variables 

  • Dummy Variable Regression
  • Interpretation of models containing indicator/Dummy variables
  • Piecewise regression
  • Related Application

    7. More Diagnostic Measures and Remedial Measures for Lack of Fit

  • Variance Inflation Factors
  • Ridge Regression
  • Deleted Residuals
  • Influence statistics – Hat matrix, Cook’s D and related measures
  • Related Application

    8. Examining All Possible Regressions

  • R2, MSE , Cp
  • Stepwise algorithms
  • Related Application

    9. Nonlinear Regression      

  • Logistic and Poisson regression models
  • Probit Model, Tobit Model
  • Related Application

Reference

  1. Draper, N.R. and Smith, H. (1999). Applied Regression Analysis. 3rd Wiley
  2. Kutner, Nachtsheim, and Neter (2004). Applied Linear Regression Models. 4th Edition, McGraw Hill
  3. Weisberg,S. (2005). Applied Linear Regression. 3rd Edition, Wiley
  4. Gujarati, Damodar N, Basic econometrics.  4th ed. Publisher: Neu delhi ; Tata McGraw-Hill, c2003
Credits 4
Pre-requisite

AST- 503
Description

  • A theoretical treatment of statistical inference (sufficient statistics, minimal sufficient statistics, ancillary statistics, complete statistics)
  • Point estimation methods and properties
  • Interval estimation
  • Hypothesis testing
  • Asymptotic evaluation
  • Estimation and hypothesis testing in regression
  • Analysis of variance
  • Chi-square tests
  • Non-Parametric Tests
  • Bayesian techniques

Text book              

Hogg, R.V. McKean, J. and Craig, A.T. (2012). Introduction to Mathematical Statistics. 7th Edition. Pearson Education, Limited

References

  1. Mood, A.M., Graybill, F.A. and Boes. D.C. (1974). Introduction to the Theory of Statistics. 3rd McGraw-Hill.
  2. Casella G, and Berger RL (2002), Statistical Inference, 2nd Brooks/Cole.
  3. Kvam, P.H. and Vidakovic B. (2007). Nonparametric Statistics with Applications to Science and Engineering.
  4. Sprent, P. and Smeeton, C. (2001). Applied Nonparametric Statistical Methods.3rd Edition. Chapman & Hall/CRC.
  5. Kendall, M., Stuart, A. and Ord, J.K. (1998). Kendall’s Advanced Theory of Statistics, Distribution Theory. Vol 1. 6th Edition. Oxford University Press, USA
  6. Kendall, M., Stuart, A. and Ord, J.K. (1999). Kendall’s Advanced Theory of Statistics, Classical Inference and the Linear Model. Vol 2. 6th Edition. Oxford University Press, USA
Credits 3
Pre-requisite

AST- 504
Description

Introduction, Preview of Linear Models and Analysis of Variance Models, One Way of Classification, Partition of Sum of Squares, Mean Squares and Expectations, Fixed and Random Effect Models, Tests, Intra-class Correlation and Variance Ratio Confidence Intervals, Analysis of Variance for Unbalanced Data, Estimates, Confidence Intervals, Inference about Difference between Treatment Means, Multiple Comparisons, Effects and Tests of Departures from Assumptions Underlying the Analysis of Variance Model,  Two Way Crossed Classification without Interaction, Model, Assumptions, Mean Squares and Expected Mean Squares, Fixed Effects, Random Effects, Mixed Effects, Tests, Two Way Crossed Classification with Interaction. Model, Assumption, Partition of SS, Mean Squares and Expectations, Fixed Effect, Random Effect and Mixed Effects, Tests, Models for Unbalanced Data.

Two Way Nested (Hierarchical) Classification, Model, Assumptions, Fixed Effects, Random Effects and Mixed Effects, Estimation and Tests, Multivariate Analysis of Variance, Repeated Measures Data and ANOVA, Multilevel Models

References

  1. Rencher, A.C. (2000). Linear Models in Statistics. John Wiley and Sons, New York
  2. Sahai, H. and Ageel, M.I. (2000). The Analysis of Variance. Birkhauser, Boston
  3. Christensen, R. (1998). Analysis of Variance, Design and Regression. Chapman and Hall, London
  4. Sahai, H. and Ojeda, M.M. (2004). Analysis of Variance for Random Models. Birkhauser, Boston
  5. Montagomery D. C. (2001): Design & Analysis of Experiments. 5th Edition. Wiley
Credits 4
Pre-requisite

AST- 505
Description

Statistical analysis using R or SAS for the following topics-

  • Multivariate analysis
  • Principal component analysis
  • Factor analysis
  • Cluster analysis
  • Profile analysis
  • Other multivariate analysis
  • Generalized Estimating Equation
  • Generalized Linear Model
  • Advance linear regression analysis
  • Non-linear regression analysis
  • Model fitting and tests.
  • Large data management

Reference:

  1. Johnson, R.A. and Wichern, D.W. (2007). Applied Multivariate Statistical Analysis. 6th Prentice-Hall
  2. Dalgaard, P. (2008). Introductory Statistics with R. Springer, 2nd Edition, ISBN 978-0387-79053-4
  3. Everitt, B. and Hothorn, T. (2006). A Handbook of Statistical Analyses Using R. Chapman & Hall/CRC, Boca Raton, FL. ISBN 1-584-88539-4
  4. Der, G. and Everitt, B.S. A Handbook of Statistical Analysis Using SAS. 3rdCRC Press
Credits 4
Pre-requisite

AST- 506
Description

  • Comparisons of several multivariate means: paired comparisons and a repeated measures design; comparing mean vectors from two populations;
  • comparison of several multivariate population means (one-way MANOVA); simultaneous confidence intervals for treatment effects; two-way multivariate analysis of variance;
  • profiles analysis; repeated measures designs and growth curves;
  • Multivariate linear regression models: the classical linear regression model; least squares estimation;
  • inferences about regression model; inferences from the estimated regression function; model checking;
  • Multivariate multiple regression; comparing two formulations of the regression model; principal components
  • factor analysis
  • canonical correlation analysis
  • Discrimination and classification
  • Cluster analysis

Text Book

1.  Johnson, R.A. and Wichern, D.W. (2007). Applied Multivariate Statistical Analysis. 6th Edition. Prentice-Hall

Credits 4
Pre-requisite

AST- 507
Description

  • Introduction to the Concepts of Modeling,
  • Model Fitting: Examples, Some Principles of Statistical Modeling (Exploratory Data Analysis, Model Formulation, Parameter Estimation, Residuals and Model Checking), Estimation and Tests Based on Specific Problems
  • Sampling Distribution for Score Statistics, MLEs, Deviance; Log-likelihood ratiom Statistic,
  • Exponential Family and Generalized Linear Models (Bernoulli, Binomial, Poisson, Exponential, Gamma, Normal, etc.),
  • Properties of distributions in the exponential family, expected value, variance, expected value and variance of score statistic, examples for various distributions.
  • Components of Generalized Linear Models- Random, Systematic and Link Functions, Poisson Regression.
  • Maximum Likelihood Estimation Using Chain Rules.
  • Random Component, Mean and Variance of the Outcome Variable, Variance Function, Dispersion Parameter, Applications.
  • Systematic Component and Link Function: Identity Link, Logit Link, Log Link, Parameter Estimation.
  • Score Function and Information Matrix, Estimation Using the Method of Scoring, Iteratively Reweighted Least Squares.
  • Inference Procedures, Deviance for logit, identity, log link functions, Scaled Deviance, Sampling Distributions, Hypothesis Testing.
  • Generalized Pearson Chi square Statistic, Residuals for GLM, Pearson Residual, Anscombe Residuals.
  • Logit Link Function, Iteratively Reweighted Least- Squares, Tests;
  • Nominal and Ordinal Logistic Regression.
  • Goodness of Fit Tests, Hosmer-Lemeshow Test, Pseudo R square, AIC and BIC.
  • Quasi Likelihood, Construction of quasi likelihood for correlated outcomes, Parameter Estimation, Variance-Covariance of Estimators, Estimation of Variance function.
  • Quasi Likelihood Estimating Equations, Generalized Estimating Equations for Repeated Measures Data, Repeated Measures Models for Normal data, Repeated Measures Models for Non-Normal Data, Working Correlation Matrix, Robust Variance Estimation or Information Sandwich Estimator, Hypothesis Testing.
  • Comparison between Likelihood and Quasi Likelihood Methods, Mixed Effect Models.

References

  1. Dobson, A.J. and Barnett, A.G. (2008). An Introduction to Generalized Linear Models. 3rd Chapman and Hall/CRC, Florida
  2. McCullagh, P. and Nelder, J.A. (1989). Generalized Linear Models. 2nd Edition, Chapman and Hall, New York.
  3. Hosmer,D.W., Lemeshow, S. and  Sturdivant, R.X. (2013). Applied Logistic Regression. 3rd Edition. Wiley, New York.

 

Credits 4
Pre-requisite

AST- 508
Description

  • Introduction: Examples, simple descriptive techniques, trend, seasonality, the correlogram. White noise (WN), Transformation to stationarity, Stationary Time series with practical examples.
  • Probability models for time series: stationarity. Moving average (MA), Autoregressive (AR), ARMA, ARIMA, SARIMA models with applications to economics, engineering and biomedical sciences.
  • Estimating the autocorrelation function and fitting ARIMA models.
  • Forecast-ing: Exponential smoothing, Forecast-ing from ARIMA models.
  • Stationary multivariate models: Stationary multivariate models with application to real life data. Dynamic simultaneous equations models, Vector autoregression (VAR) models, Granger causality, Impulse response functions, Variance decompositions, Structural VAR
  • Nonstationary Multivariate models: Nonstationary Multivariate models with examples. Spurious regression, Cointegration, Granger representation theorem, Vector error correction models (VECMs), Structural VAR models with cointegration, testing for cointegration, estimating the cointegrating rank, estimating cointegrating vectors.
  • Stationary processes in the frequency domain: The spectral density function, the periodogram, spectral analysis with Empirical aspects of spectral analysis State-space models: Dynamic linear models and the Kalman filter with applications of filter.

 References

  1. Robert H. Shumway and David S. Stoffer (2010): Time Series Analysis and Its Applications With R Examples.3rd Springer. ISBN: 9781441978646
  2. Box, G.E.P. Jankins, G.M. and Reinsel G.C. (2008): Time series Analysis (Forecasting and control). 4th edition, Wiley
  3. Cryer, J.D. and Chan K.S. (2009): Time Series Analysis with Applications in R. 2nd Edition, Springer
  4. Chatfield, C. (2003): The Analysis of Time Series: An Introduction. 6th Edition. Chapman & Hall/CRC
  5. Brockwell, P.J. and Davis, R.A. (2009). Time Series: Theory and Methods. 2nd Springer
  6. Wheelwright, S.C. and Makridakis, S. G. (1989). Forecasting Methods for Management, 5th Wiley, New York.
  7. Anderson, T.W. (1971). The Statistical Analysis of Time series. 1st Edition. John Wiley, New York

 

Credits 4
Pre-requisite

AST- 509
Description

Review of: Contingency table, Inference of contingency table, GLM for binary and count data, Inference of logistic regression.
Logit Models for Multinomial Responses
Nominal Responses: Baseline-Category Logit Models; Ordinal Responses: Cumulative Logit and link Models; Alternative Models for Ordinal Responses; Testing Conditional Independence in I×J×K Tables; Discrete-Choice Multinomial Logit Models.
Loglinear Models for Contingency Tables
Loglinear Models for Two-Way Tables; Loglinear Models for Independence and Interaction in Three-Way Tables; Inference for Loglinear Models; Loglinear Models for Higher Dimensions; The Loglinear_Logit Model Connection.
Building and Extending Loglinear / Logit Models
Modeling Ordinal Associations; Association Models; Association Models, Correlation Models, and Correspondence Analysis; Poisson Regression for Rates; Empty Cells and Sparseness in Modeling Contingency Tables.
Models for Matched Pairs
-Comparing Dependent Proportions, Conditional Logistic Regression for Binary Matched Pairs, Marginal Models for Square Contingency Tables, Symmetry, Quasi-symmetry, and Quasi independence, Measuring Agreement between Observers, Bradley Terry Model for Paired Preferences, Marginal Models and Quasi-symmetry Models for Matched Sets.
Analyzing Repeated Categorical Response Data
-Comparing Marginal Distributions: Multiple Responses, Marginal Modeling: Maximum Likelihood Approach, Marginal Modeling: Generalized Estimating Equations Approach, Quasi likelihood and Its GEE Multivariate Extension Details, Markov Chains: Transitional Modeling.

Reference Book:

  • Agresti A. (2012).Categorical Data Analysis. 3rd Edition. Wiley

 

Credits 4
Pre-requisite

AST- 510
Description

  • Review on Parametric Regression Models for Lifetime Data: Introduction, graphical methods for model selection, inference for log-location scale models, and extension of log-location scale models.
  • Semi-parametric Multiplicative Hazards regression Model: Introduction, estimation of parameters, inclusion of strata, time-dependent covariates, residuals and model checking, methods for Grouped or discrete lifetimes, related topics on the Cox model.
  • Rank-Type Procedures for Log-Location-Scale models: Rank tests for comparing distributions, estimation for semi-parametric accelerated failure time models.
  • Multiple Modes of Failure: Basic characteristics of model specification, likelihood functions formulation, nonparametric methods, parametric methods, semi-parametric methods for multiplicative hazards model.
  • Logistic regression, Goodness of fit test, Test of fit of regression model: Location-scale regression models.
  • Analysis of Correlated Lifetime Data: Introduction of regression models for correlated lifetime data, representation and estimation of bivariate survivor function.

References:

  1. Lawless, J.F. (2003). Statistical Models and Methods for Lifetime Data. 2nd Edition. Wiley
  2. Kalbfleisch, J.D. and Ross, L.P. (2002). The Statistical Analysis of Failure Time Data, 2nd Edition. Wiley
Credits 4
Pre-requisite

AST- 511
Description

  1. Review of Analysis of variance (ANOVA) for Fixed, Random and Mixed effect models with and without Interaction.
  2. Analysis of co-variance: one–way and two–way classifications. Estimation of main effects, interactions and analysis of 2k factorial experiment in general with particular reference to k = 2, 3 and 4 and 32 factorial experiments. Multiple comparisons, Fisher LeAST- Significance Difference (L.S.D) test and Duncan’s multiple range test (DMRT).
  3. Total and partial confounding in case of 23, 24 and 32 factorial designs. Concept of balanced partial confounding. Fractional replications of factorial designs – one-half replication of 23& 24 design, one-quarter replication of 25& 26 Split–plot design.
  4. Balanced incomplete block design (BIBD) – parametric relations, intra-block analysis, recovery of inter-block information. Partially balanced incomplete block design with two associate classes PBIBD (2) – Parametric relations, intra block analysis. Simple lattice design and Youden-square design
  5. Concept of Response surface methodology (RSM), the method of steepest ascent. Response surface designs. Design for fitting first – order and second – order models. Variance of estimated response. Second order rotatable designs (SORD), Central composite designs(CCD): Role of CCD as an alternative to 3k design, Annotatability of CCD

 References:

  1. Sahai, H. and Ageel, M.I. (2000). The Analysis of Variance: Fixed, Random and Mixed Models. 2000th Birkhauser
  2. Christensen, R. (1996). Analysis of Variance, Design and Regression. Chapman and Hall/CRC, London
  3. Rencher, A.C. and Schaalje G.B. (2008). Linear Models in Statistics.2nd Edition Wiley -Interscience, New York
  4. Sahai, H. and Ojeda, M.M. (2013). Analysis of Variance for Random Models. 1st Edition, Birkhauser, Boston
  5. Montagomery, D. C. (2012): Design & Analysis of Experiments. 8th Wiley
  6. Dean A.M. and Voss D (2001). Design and analysis of experiments. Corrected Edition. Springer.

 

Credits 4
Pre-requisite

AST-512
Description

Understanding Environmental Pollution:  Pollution and its Importance, Why does Pollution happen, Pollutant Sources, Detail Study of Air and Water Pollution, Global Climate Change Environmental Standards: Concept of Environmental Standards, Statistically Verifiable Ideal Standard (SVIS), Guard Point Standards, Standards along Cause-Effect Chain.

Stochastic Process in Environment: Applications of Bernoulli, Poisson and Normal Process to Environmental problems.

Environmental Sampling: Network Sampling, Composite Sampling, Ranked-set Sampling,  Quadrat sampling, Capture-Recapture sampling, Transect sampling, Line Transects and variable circular plots, Density Estimation, Method of line transects, Spatial distribution and prediction, Spatial Point process models and methods.

Diversity: Measurement of diversity, Different diversity indices.

Diffusion and Dispersion of Pollutants: Wedge Machine, Particle Frame Machine, Plume Model.

Dilution of Pollutants: Deterministic Dilution, Theory of Successive Random Dilution (SRD), Application of SRD to Environmental Phenomena: Air Quality, Indoor Air Quality, Water Quality, Concentrations of Pollutants in Soils, Plants and Animals, Concentration in Food and Human Tissue.

Statistical Theory of Rollback: Predicting concentrations after Source Control, Correlation, Previous Rollback Concepts, Environmental Transport Models in Air and Water.

Environment and economics: Theory of Environmental Externalities, Coase Theorem, Environmental Welfare analysis, Trade and Environmental policy, Resource allocation over time, valuing the environment, Cost-benefit analysis, Allocation of resources, Renewable and Non-renewable resources.

 

Text Book

  • Barnett, V. (2004). Environmental Statistics: Methods and Applications, John Wiley and Sons, New York.

References

  1. Bryan, F. J. (2000). Statistics for Environmental Science and Management. 1st Edition, Chapman and Hall/ CRC, Press
  2. Millard, S.P. and Neerchal, N.K. (2000). Environmental Statistics Using S-Plus. Chapman and Hall/CRC Press
  3. John, T. (2003). Practical Statistics for Environmental and Biological Scientists. John Wiley and Sons, New York
  4. Robert, H. (1990).Spatial Data Analysis in the Social and Environmental Sciences. Cambridge University Press, Cambridge Articles from different Journals.

 

Credits 3
Pre-requisite

AST- 513
Description

  1. A methods curse in statistic aspects of reliability. Topics include: application of normal, lognormal, exponential, weibul models to reliability problem; censored; probability and hazard plotting; series system and multiple failure models, maximum likelihood estimation; introduction to accelerated life models and analysis.
  2. Coherent Systems: Reliability concepts – Systems of components. Series and parallel systems – Coherent structures and their representation in terms of paths and cuts, Modular decomposition.
  3. Reliability of coherent systems – Reliability of Independent components, association of random variables, bounds on systems reliability and improved bounds on system reliability under modular decomposition.
  4. Life Distribution: Survival function – Notion of aging IFR, DFR, DFRA, NBU and NBUE classes, Exponential distributions and its no-ageing property, ageing properties of other common life distribution, closures under formation of coherent structures, convolutions and mixtures of these cases.
  5. Maintenance and replacement policies, relevant renewal theory, availability theory, maintenance through spares and repair.
  6. Reliability estimation: Estimation of two and three parameter Gamma, Weibull and log normal distributions

References

  1. Barlow, R.E. and Proschen, F. (2007). Statistical Theory of Reliability and life testing. 2nd Halt, Reinhart and Winston Inc
  2. Barlow and Proschen (1996). Mathematical Theory of Reliability. SIAM Edition. John Wiley
  3. (2010). Reliability Engineering, 10th Edition,Tata Mc Graw Hill.
  4. J. (1980). Statistical Analysis of Reliability and like testing Models. Marcel Decker, New York.
  5. Sinha, S.K., and Kale, S.K., (1980). Life testing and Reliability Estimation. Wiley Eastern.

 

Credits 3
Pre-requisite

AST- 514
Description

Epidemiologic Research, Etiologic Research, Experiments, Quasi Experiments, Observational Studies, lifetime distribution, continuous model, discrete model, hazard function, Survival function, regression models, Subject selection, Methods of observation, Ratio measures, Difference measures, Basic Designs: Cohort study, cross-sectional study, case-control study, Hybrid designs, incomplete designs

Measures of Disease Frequency: Describe the key aspects of measuring disease occurrence, Basic incidence measures; risk and rate, Estimation of average rates, Estimation of risk, Prevalence measures, Mortality measures, mathematical relationship between the measures of diseases frequency, provide examples of commonly used measures of diseases frequency in public health.

Identifying Non-causal Associations, Confounding: The nature of association between the confounder, the exposure and the outcome, risk factors, single risk factor confounding; Confounding involving several risk factors; definition of joint confounding, variable selection, Assessing the presence of confounding, control of confounding, Additional issue related to confounding.

Selection Bias and Information Bias: General Formulation, Direction of selection bias, Example of selection bias, Examples of misclassification in only the outcome variable, general formulation of misclassification bias, independent misclassification of both exposure and disease.

Multivariate Analysis in Epidemiology: Stratification and Adjustment techniques to Disentangle confounding, Adjustment Methods based on stratification, Multiple Regression Techniques for Adjustment, Alternative approaches for the control of confounding, Incomplete adjustment: Residual Confounding, over adjustment, Logistic regression analysis: follow-up and case-control studies, logistic modeling: Application to real life data, Applications of logistic regression with interaction, using unconditional ML estimation.

Epidemiological issues in the interface with public health policy: Introduction, Causality: Application to public health and health policy, Decision tree and Sensitivity analysis, Meta-Analysis, Publication bias.

Reference:

  1. Kleinbaum, D.G., Kupper, L.L. and Morgenstern, H. (1982). Epidemiologic Research: Principles and Quantitative Methods.
  2. Rothman, K.J., Lash, T.L. and Greenland, S. (2012). Modern Epidemiology. 3rd Lippincott Williams and Wilkins, USA.
  3. Szklo, M. and Nieto, F.J. (2012).Epidemiology, Beyond the Basics. 3rd Edition, Jones & Bartlett Learning.
  4. Lawless, J.F. (2002). Statistical Models and Methods for Lifetime Data. 2nd Wiley-Interscience.

 

Credits 3
Pre-requisite

AST- 515
Description

Methods of Population Analysis: Rates, Ratios, Proportions, Percentages, Person, Months/Year, Incidence, Prevalence, Rates of Population Growth, Cohort and cross-sectional indicators, Crude rates and standardized methods, Methods of Population projections, Inter-censal/ postcensal estimates of population.

Population Aging:  Elderly Situation, Aging Index, Support Ratio Index, Care Index, Elderly Situation in Bangladesh, Components (Elements) of Aging Policy in Bangladesh, Goals and Objectives of Aging Policy in Bangladesh.

Gender Preference: Family Size, Ideal Family Size, Sex Preference of Family Size, Factors Affecting Sex Preference in Bangladesh, Relationship between Actual Fertility and Ideal Fertility, Fertility of Spacers and Limiters and their effect, Effect of under five mortality or infant mortality on Desired Family Size.

Decomposition of Change in TFR between two Time Periods: Bongaart’s Model, Target setting by Bongaarts Model, Relationship between Fertility and Contraceptive use.

Population Stabilization: Population Stabilization, Tempo Effect, Quantum Effect, Implication of Population Stabilization if Replacement Fertility is not Achieved, Population Momentum, Reduction of Population Momentum, Factors to be Considered in Reduction Population Momentum.

Demographic Benefits: Achieved Replacement Fertility in Time, Its Benefit in falling Fertility, Demographic Window/Bonus: Implication of Macro Economic Growth.

Population Policies and in Bangladesh: History of growth of population in Bangladesh; Implications of the growth of population in Bangladesh; Population policy in Bangladesh; Level, trends and determinants in fertility, mortality and migration in Bangladesh; Interrelationship between population and development; Future prospects of population and population control in Bangladesh; Aged and aging of population in Bangladesh;

References:

  1. Shryock et al (2004). The methods and materials of demography. Volume I and II.U.S, Department of Commerce Publication.
  2. Chiang, C. L. (1984). The Life Table and Its Applications. Krueger Pule, John Wiley, New York.
  3. Bongaarts, J. and Potter, R.G. (1982). Potter Fertility. Biology and Behaviour: AnAnalysis of the Proximate Determinants of Fertility. Academic Press, Sandiego, California.
  4. Colin, N. (1988). Methods and Models in Demography. Belhaven Press, London.
  5. Selected articles from Population Studies, Demography. Population and Development Studies in Family Planning etc.
  6. SmithD, KeyfitzN. (2011): Mathematical Demography. Springer
Credits 3
Pre-requisite

AST- 516
Description

  1. Multicollinearity: nature, detection, consequence and remedy of multicollinearity
  2. Autocorrelation 
  3. Heteroscedasticity
  4. Model Specification: Consequences of under and over specification, model selection criteria
  5. Estimation and application of Cobb-Doglas production function
  6. Simultaneous equation models :
    • Simultanious equation bias
    • Inconsistance of OLS estimations
    • Types and rules of identification
    • Estimation of simultanious estimation methods: Methods of idirect leAST- square(ILS) and two stage least square(2SLS)

       7.Non-Linear regression:

  • Least Square Estimation,
  • Estimating the Parameter: Response surface methodology, Semilogarithm
  • Time series Econometrics: Stationarity, Unit roots and co-integration, Spurious regression, Dynamic Econometrics model, Distributed lag models.

     8. Panel Data Models:

  • Fixed Effects
  • Random Effects
  • Dynamic Model

References:

  1. H. Greene (2011). Econometric Analysis. 7th Edition. Prentice Hall.
  2. M. Wooldridge (2010). Econometric Analysis of Cross Section and Panel Data. 2nd Edition. The MIP Press.
  3. M Verbeek (2000). A guide to Modern Econometrics. 3rd Edition, John Wiley & Sons

 

Credits 3
Pre-requisite

AST- 517
Description

  • Simple and multiple regression models;
  • point estimation in the general linear model,
  • projection operators,
  • estimable functions and generalized inverses;
  • Tests of general linear hypotheses; Diagnostics and Remedial Measures.
  • power;
  • Matrix Approach of the general linear model
  • Quadratic Forms and Their Distributions,
  • General Linear Models, General Framework,
  • Least Squares,
  • Properties of Estimators,
  • Gauss-Markov Theorem,
  • analysis of variance (ANOVA)
  • analysis of covariance models (ANOCOVA)
  • Interval Estimates of Parameters, Testing of Hypothesis, Diagnostics and Remedial Measures
  • Generalized Least Squares,
  • Extra Sums of Squares,
  • Estimation and Hypothesis Testing for Full Rank and Less than Full Rank Models, Model Selection Criteria,
  • fixed, random, and mixed effects model;
  • Correlation;
  • methods for simultaneous inference ;
  • residual analysis and checks of model adequacy

Text books 

  1. Rencher, A.C. (2000). Linear Models in Statistics. Wiley, New York
  2. Seber, G.A.F. (1977). Linear Regression Analysis. Wiley, New York

 

References

  1. Guttman, I. (1982). Linear Models: An Introduction. Wiley, New York.
  2. Draper, N.R. and Smith, H. (1998): Applied Regression Analysis; 3rd Edition, Johan Wiley and Sons
  3. McCullagh, P. and Nelder, J.A. (1989). Generalized Linear Models. Chapman Hall, New York
  4. Ryan, T.P. (1997). Modern Regression Methods. Wiley, New York
  5. Fox, J. (1997). Applied Regression Analysis, Linear Models, and Related Methods. Sage, Thousand Oaks, Ca
  6. Neter, J., Wasserman, W. and Kutner, M.H. (1990). Applied Linear Statistical Models. 3rd Irwin, Boston.
  7. Gujarati, D.N. (2004): Basic Econometrics. 4th Edition. Mc Graw-Hill  Inc
Credits 3
Pre-requisite

AST- 518
Description

  1. Introduction to Epidemiology and Clinical Trials, brief history of clinical trials
  2. Phase I and II clinical trials
    a.Phase I dosing trials, Clinical pharmacology
    b.Phase II clinical trials (screening and feasibility): Review of confidence intervals, Gehan’s two-stage design, Simon’s two-stage sequential design
  3. Phase III clinical trials fundamentals
    a.Issues to consider before designing a clinical trials
    b.Ethical Issues
    c.Randomized clinical trials
  4.  Randomization
    a.Design based inference
    b.Fixed allocation randomization
    c.Adaptive randomization
    d.response adaptive designs
  5. Additional issues in Phase III clinical trials
    a.Single blind and double blind
    b.Use of placebo controlled trials
    c.The protocol document
  6. Sample size calculations
    a.Test for equality – Continuous: T-test for two-sample comparison, ANOVA- F-tests
    b.for K-sample comparisons
    c.Test for equality – Categorical: Proportions test for two-sample comparisons, Arc-sin square root transformation to stabilize variance, Chi-square test for K-sample comparisons.
    d.Test for equivalency
  7. Causality, non-compliance and intent-to-treat
    a.Causality and counterfactual random variables
    b.Noncompliance and intent-to-treat analysis
    c.A causal model with noncompliance
  8. Survival analysis in Phase III clinical trials
    a.Distribution of time to event
    b.Life-table methods and Kaplan-Meier estimator
    c.Log rank tests for two and K-sample comparisons
    d.Power and sample size considerations
    e.Multiple comparisons
  9. Early stopping of clinical trials
    a.General issues in monitoring clinical trials
    b.Information based design and monitoring
    c.Type I error – equal increments of information
    d.Choice of boundaries: Pocock boundaries, O’Brien-Fleming boundaries
    e.Power and sample size calculation: Inflation factor, Information based monitoring,
    f.Average information, Group sequential tests with equal increments of information

 References:

  1. Steven P. (2005). Clinical Trials: A Methodologic Perspective. 2nd Edition. Wiley Interscience
  2. Friedman, L.M., Furberg, C.D. and De Mets, D.L. (1999). Fundamentals of Clinical Trials. 3rd Edition .Springer

 

Credits 3
Pre-requisite

AST- 519
Description

Review of Survival Models, Life tables and Selection, Multiple State Models, Joint Life and last Survivor benefits

Pension mathematics: Summary, Salary Scale Function, Valuation of Benefits, Service table

Yield curves and Non-diversifiable Risk: Yield Curve, valuation of Insurances and Life annuities, Diversifiable and non-diversifiable Risk, Monte Carlo Simulation

Emerging Costs for Traditional Life Insurance: Introduction, profit testing a term insurance policy, Profit testing Principles, Profit measures, Profit testing Multiple State Models Simulation: The Inverse Transform method, The Box Muller method, The Polar method

References:

  1. Dickson, D.C.M. Hardy, M.R. and Waters, H.R (2013). Actuarial mathematics for life contingent risks. 2nd Cambridge University Press.
  2. Benjamin, B. and Pollard, J.H. (1993). The Analysis of Mortality and other Actuarial Statistics. 3rd Institute and Faculty of Actuaries.
  3. Jordan, C.W. (1975). Life Contingencies. 2nd Edition. Chicago: Society of Actuaries

 

Credits 3
Pre-requisite
+ Bachelor of Science in Applied Statistics

The BS in Applied Statistics Program

 

Minimum Requirement for the degree of BS in Applied Statistics 127 credits.

A student must accumulate a minimum of 127 credit hours, with a minimum of the indicated numbers of credit hours from sections I-IV, in order to obtain the degree. The sections and the indicated required credit hours are as the following.

Section Description Credit Hours
I Language and General Education Requirements 21
II Mathematics & Economics  15
III Applied Statistics Core
Courses
91
Total 127

Section I. General Education Requirements (21 Credit Hours)

Section I A: Compulsory General Education Courses (Three courses: 9 credit hours)

Section I B: Optional General Education Courses (2 courses, OPT001 and OPT002).

For Applied Statistics, students should choose Gen 239 and one more course from the following list; a total of 3+3=6 Credit Hours.   

Section I C: Optional Courses from Business & Relevant Subject (2 courses, OPT003 and OPT004). Applied Statistics students may choose any two courses: 3+3=6 credit hours).

Section II: Mathematics and Economics  (15 Credit Hours)

These courses stress the fundamental principles upon which the applied statistics subject is based. Applied Statistics students must take a total of 15 credit hours).

Course Number/Course title Credit Hours
MAT101: Differential & Integral Calculus 3
MAT 102: Differential Equations & Special Functions 3
MAT 206: Basic Algebra and Linear Algebra 3
ECO101:  Principles of Microeconomics 3
ECO102: Introduction to Macroeconomics 3
Total 15

Section III. Applied Statistics Core Courses (91 Credit Hours)

The following courses stress fundamental Applied Statistics concepts.

Course No. Course Title Credits
AST – 101 Introduction to Statistics 3
AST – 102 Elements of Probability 3
AST – 201 Probability Distributions 3
AST – 202 Sampling Distributions 3
AST – 203 Statistical Inference I 3
AST – 204 Agricultural Statistics and Design of Experiments 3
AST – 205 Introduction to Demography 3
AST – 206 Introductory Sampling Methods 3
AST – 207 Applied Statistical Analysis with R (Lab) 3
AST – 301 Design and Analysis of Factorial Experiments 3
AST – 302 Advanced Sampling Techniques 3
AST – 303 Statistical Inference II 3
AST – 304 Applied Regression Analysis 3
AST – 305 Introduction to Epidemiology 3
AST – 306 Population Studies 3
AST – 307 Social Statistics and Social Development 3
AST – 308 Statistical Analysis Using SPSS and SAS (Lab) 3
AST – 309 Applied Nonparametric Statistics 3
AST – 310 Categorical Data Analysis 3
AST – 401 Advanced Probability and Stochastic Process 3
AST – 402 Research Methodology 4
AST – 403 Applied Multivariate Data Analysis 3
AST – 404 Survival Analysis I 3
AST – 405 Industrial Statistics and Operation Research 3
AST – 406 Modeling Time Series Data 3
AST – 407 Introduction to Generalized Linear Models 3
AST – 408 Life Contingencies I 3
AST – 409 Bayesian Inference and Decision Theory 3
AST – 410 Statistical Analysis using STATA (Lab) 3
AST – 499 Project Report and Seminar 3
  Total 91

AST-101
Description

Statistics and its origin:
Defining Statistics, Characteristics of Statistics, Uses & Importance of Statistics, Population & Sample, Sources of Statistical Data, Parameter and Statistic
Summarizing Data:
Meaning of Data, Level of Measurement, Variable and attribute, Summarizing and Presenting Data, Frequency Distribution, Formation of Discrete and Continuous Frequency Distribution, Cumulative Frequency Distribution, Presenting Data by Graphs and Diagrams, Presentation of Qualitative Data, Presentation of Quantitative Data.
Descriptive Statistics I: Measures of Central Tendency
Measures of central tendency, arithmetic mean, median, quartiles, percentiles and deciles, mode, geometric mean, harmonic mean, other measures of average, comparing the averages, properties of measures, effects of change in origin and scale, stem and leaf plot
Descriptive Statistics II: Measures of Dispersion
Meaning of dispersion, measures of dispersion, absolute measures of dispersion, relative measures of dispersion, empirical relations among measures of dispersion, comparing the measures, moments, central moments in terms of raw moments, effects of change in origin and scale on moments, Sheppard’s correction for moments, shape characteristics of a distribution, box and whisker plots.
Simple Linear Regression and Correlation:
Correlation analysis, measuring the correlation, rank correlation, regression analysis, simple linear regression model, scatter diagram, Least- square method, properties of regression coefficient, partitioning of the total variation in regression, Coefficient of multiple determination

Credits 3

AST-102
Description

Mathematical logic: propositional calculus, predicate calculus. Set theory: sets, relations, partial ordered sets, functions. Counting: Permutations, Combinations, principles of inclusion and exclusion. Discrete Probability. Algorithm and Growth of functions. Mathematical reasoning: induction, contradiction, recursion. Recurrence Relations. Graph theory: graphs, paths, trees. Algebraic structures: binary operations, semi groups, groups, permutation groups, rings and fields, lattices.

Credits 3
 

Description

Credit-3

  • Random variables; probability mass function, cumulative density function and probability density function
  • Discrete Probability Distributions: Bernoulli, binomial, Poisson, geometric, negative binomial, Hypergeometric, uniform
  • Continuous Probability Distributions: uniform, exponential, gamma, beta, normal, log- normal,Weibull
  • Identification of Moment and cumulant generating functions; characteristic function of discrete and continuous distributions
  • Showing moments from Moment and cumulant generating functions; characteristic function
  • Distribution of a function of a random variable from the distribution of a random variable
  • Determination of probability generating function of discrete and integer-valued random variables
  • Application of PGF, MGF, CGF and cumulants and the reason of their use
  • Joint, Marginal and conditional distributions
  • Law of large numbers; and central limit theorem.
  • Cauchy-Schwartz, Markov and Chebysheb inequality
Credits 3
Pre-requisite MAT101, AST-101, AST-102

AST-203
Description
Credit-3
Methods of finding estimators: methods of moments, maximum likelihood, and other methods;
Properties of point estimators: closeness, mean-squared error, loss and risk functions;
Sufficiency: sufficient statistics, factorization criterion, minimal sufficient statistics, ancillary statistics;
Completeness: complete statistics, exponential family;
Likelihood Functions
Parameter Estimation(point and interval):
Linear estimation
Maximum Likelihood estimation
Bayesian estimation
Large sample properties and procedures
Empirical distribution function
Introduction to test of hypothesis : Best critical region, Most powerful tests, Concept of confidence interval, Confidence interval for parameters

Credits 3
Pre-requisite AST-101, AST-102

AST-204
Description

Agricultural statistics: definition and application; basic and current agricultural statistics; estimation of mean yields; crop cutting experiment; crop forecasting; livestock; sample survey.

Census of agriculture: objectives; scope; coverage; concepts and definitions. Statistics of selected agricultural crops; index number of agricultural production; weights, indices used;

Design of experiments: some typical examples of experimental design; basic principles;

the analysis of variance; analysis of fixed effects, random effect and mixed effect model; estimation of model parameters; unbalanced data; model adequacy checking; regression model, comparisons among treatment means, graphical comparisons of means, contrasts, orthogonal contrasts, multiple testing, Scheffe’s method, comparing pairs of treatment means, comparing treatment means with a control; Determining sample size; operating characteristic curve, least squares estimation of the model parameters, normality test.
Complete randomize design(CRD), Randomized blocks design (RBD), Latin squares design (LSD), model adequacy checking; estimating model parameters; Gareco-Latin square design; balanced incomplete block design (BIBD); statistical analysis of BIBD; Least- squares estimation of BIBD; example of real life application of these methods.

Credits 3
Pre-requisite AST-203

AST-205
Description

Introduction: Basic concept of demography; Role and importance of demographic/population studies; Sources of demographic data: census, vital registration system, sample surveys, population registers and other sources especially in Bangladesh.
History: History of census taking and vital registration in the sub-continent, Uses of data from these sources; strength and weakness of data from them, Growth of population in Bangladesh since 1901.
Errors in demographic data: types of errors and methods of testing the accuracy of demographic data, Quality checking and adjustment of population data. Post enumeration check (PEC) and detection of errors and deficiencies in data and the needed adjustments and corrections.
Fertility: Basic measures of fertility. Crude birth rate, age specific fertility rates (ASFR), general fertility rate (GFR), total fertility rate (TFR), gross reproduction rate (GRR) and net reproduction rate (NRR), child-woman ratio, Concept of fecundity and its relationship with fertility.
Demographic theory:Transition theory and the present situation in Bangladesh, Malthus’ theory and its criticism. Mortality: Basic measures of mortality: crude death rate (CDR), age specific death rates (ASDR), infant mortality rate, child mortality rate, neo-natal mortality rate, Standardized death rate its need and use, Direct and indirect standardization of rates, Commonly used ratios: Sex ratio, child-woman ratio, dependency ratio, density of population.
Fertility and mortality in Bangladesh since 1951: Reduction in fertility and mortality in Bangladesh in recent years, Role of socio-economic development on fertility and mortality.
Nuptiality: Marriage, types of marriage, age of marriage, age at marriage and its effect on fertility, celibacy, widowhood, divorce and separation, their effect on fertility and population growth.

Migration: Definition, internal and international migration, Sources of migration data, Factors affecting both internal and international migration, laws of migration. Impact of migration on origin and destination, its effect on population growth, age and sex structure, labor supply, employment and unemployment, wage levels, and other socio-economic effects, Migration of Bangladeshis abroad and its impact on overall economic development of the country.

Credits 3
Pre-requisite AST-101

AST-206
Description

Introduction: Uses of Sample Surveys and some review of sampling design of national surveys of Bangladesh, Preliminary Planning of a Sample Survey. Different types of errors associated with sampling and complete enumeration. Declining Coverage and Response Rates, Sampling Weights, questionnaire, Design effect with real life application, sample size determination.
The Population and the Sample: The Population, Elementary Units, Population Parameters, The Sample, Probability and Nonprobability Sampling, Sampling Frames, Sampling Units, and Enumeration Units, Characteristics of Estimates of Population Parameters, Bias, Mean Square Error, Validity, Reliability, and Accuracy.
Simple Random Sampling: How to Take and apply Simple Random Sample. Estimation of Population Characteristics and Standard Errors
Systematic Sampling: How to Take and apply Systematic Sampling, Estimation of Population Characteristics, Sampling Distribution of Estimates, Variance of Estimates, A Modification That Always Yields Unbiased Estimates.
Stratification and Stratified Random Sampling: How to Take and apply Stratified Random Sample , Population Parameters for Strata, Sample Statistics for Strata, Estimation of Population Parameters from Stratified Random Sampling, Estimation of Standard Errors, Allocation of Sample to Strata, Equal Allocation, Proportional Allocation: Self-Weighting Samples, Optimal Allocation, Stratification After Sampling.
Ratio Estimation and Regression Estimation: How to apply through Real life scenarios. Approximation to the Standard Error of the Ratio Estimated Total, Determination of Sample Size, Regression Estimation of Totals.
Cluster Sampling: Real life application of cluster sampling. Simple One-Stage Cluster Sampling, Two-Stage Cluster Sampling: Clusters Sampled with Equal Probability, Choosing the Optimal Cluster Size n Considering Costs, Cluster Sampling Unequal Probability: Probability Proportional to Size Sampling, the Horvitz–Thompson Estimator, the Hansen–Hurwitz Estimator

Credits 3
Pre-requisite AST-203

AST-207
Description

A first session in R

  • Getting data into R
  • Basic data manipulation
  • Data Modeling
  • Distribution fitting
  • Basic plotting
  • Loops and functions
  • Basic stats
  • Survival Model
  • Advanced data manipulation

 

Credits 3
Pre-requisite AST-203

AST-301
Description

Introduction to Factorial Designs: Basic definition and principles; The advantage of factorials; The two-factor factorial design; statistical analysis of fixed effects model, model adequacy checking, estimating the model parameters, choice of sample size, the assumption of no interaction in a two-factor model, one observation per cell; The general factorial design; Fitting response curve and surfaces; Blocking in a factorial design.

Response Surface Methods: basic concept of response surface methodology.

Experiments with Random Factors: The two-factor factorial with random factors; The two-factor mixed model; Sample size determination with random effects; Rules for expected mean squares; Approximate F tests; Approximate confidence intervals on variance components; The modified large-sample method; Maximum likelihood estimation of variance components.
Nested and Split-Plot Designs: The two-stage nested designs; statistical analysis, diagnostic checking, variance components; General m-staged nested design; Designs with both nested and factorial factors; The split-plot design;
Analysis of Covariance: Description of the procedure; Factorial experiments with covariates.

Credits 3
Pre-requisite AST-204

AST-302
Description

Sampling with real life application of unequal clusters with unequal probability with and without replacement different selection methods: PPS selection, Raj’s, Murthy’s and Rao-Hartley-Cochran methods of selection, Two-stage sampling with equal and unequal sized clusters-estimates and standard errors; estimation for proportions; stratified two-stage sampling.
Multistage sampling: how to apply different two and three stage sampling schemes; the concept of self-weighting estimates; assumptions for self-weighting estimates;
Multiphase sampling: real life application of this technique. Two-phase or double sampling; ratio and regression estimators for double sampling and respective standard errors; double sampling for stratification. Repeated sampling; sampling from the same population on two occasions, more than two occasions. Interpenetrating sub sampling. Concept of base line survey and panel survey.
Special sampling schemes: capture-recapture method; network sampling; snowball sampling; adaptive cluster sampling; rank set sampling with application.
Re-sampling methodologies: bootstrap, Jackknife and Gibbs sampling.
Sampling and non-sampling errors: sources and types of non-sampling error; non-sampling bias; non-response error; control of non-response; techniques for adjustments of non-response; Politz-Simon’s technique; response bias and response variance.

Credits 3
Pre-requisite AST-206

AST-303
Description

Introduction to test of hypothesis
Best critical region

  • Most powerful tests
  • Likelihood ratio tests
  • Exponential family of densities
  • Sufficiency and exponential family of densities and tests
  • Sequential probability ratio test
  • Theory of confidence intervals and tests
  • Goodness of fit tests
  • Tests based on quasi-likelihood
  • Bayesian inference
  • Asymptotic distribution of LRTs and other large sample tests
Credits 3
Pre-requisite AST-203

AST-304
Description

  1. Simple Linear Regression Model
  • Model for E(Y|X), model for distribution of errors
  • Least- squares estimation
  • Estimation of variance
  1. Inferences for Simple Linear Model
  • Inferences concerning the slope (confidence intervals and t-test)
  • Confidence interval estimate of the mean Y at a specific X
  • Prediction interval for a new Y
  • Analysis of Variance partitioning of variation in Y
  • R-squared calculation and interpretation
  1. Diagnostic procedures for aptness of model
  • Residual analyses

o Plots of residuals versus fits, residuals versus x

o Tests for normality of residuals

o Lack of Fit test, Pure Error, Lack of Fit concepts

  • Transformations as solution to problems with the model
  1. Matrix Notation and Literacy
  • X matrix, vector, y vector, vector
  • (X’X)-1 X’Y estimates coefficient vector
  • Variance- Covariance matrix
  1. Multiple Regression Models and Estimation
  • extension to simple linear model
  • Interaction models
  • Basic estimation and inference for multiple regression
  • Generalized Least- Squares and Weigthed Least- Squares
  • Extra Sum of Squares Principles and related Tests
  1. Multicollinearity and Model diagnostics
  2. Selecting the Best Regression Equations
Credits 3
Pre-requisite AST-203, MAT206

AST-305
Description

Introduction: Measuring Disease Frequency, Problems of Validity, Problems in controlling for extraneous factors
Fundamentals of Epidemiologic Research: Epidemiologic Research, Etiologic Research
Types of Epidemiological Research: Experiments, Quasi Experiments, Observational Studies
Design Options in Observational Studies: Subject selection, Methods of observation
Typology of observational Basic Designs: Cohort study, cross-sectional study, case-control study, Hybrid designs, incomplete designs
Measures of Disease Frequency: Basic incidence measures; risk and rate, Estimation of average rates, Estimation of risk, Prevalence measures, Mortality measures
Measures of Association: Ratio measures, Difference measures,
Confounding: Working definition of a confounder, risk factors, single risk factor confounding; Confounding involving several risk factors; definition of joint confounding, variable selection and control of confounding.
Measures of Potential Impact and Summary of measures: Measures of potential Impact, Summary of epidemiologic measures
Validity of Epidemiologic Research: Validity and precision, Internal validity

Credits 3
Pre-requisite AST-203, AST-304

AST- 306
Description

Adjustment of demographic data: Sources and types of errors and deficiencies in data; General methods of evaluation and detection of error and deficiencies in data; Methods of checking completeness and other types of errors in demographic data and their adjustment.
Graduation of data: Meaning and its need, techniques of graduation, graduation of age distribution.
Life table: Its concept, structure and calculation, complete life table (life table by single year of age) and abridged life table, multiple decrement life tables, working life table, different life table functions and inter-relationships among them, use of life table, etc.
Force of mortality: Idea and definition calculation of life table with the help of force of mortality. Population growth, techniques to measure it, doubling time concept in demography. Population estimates and projections. Different techniques of population projection- component method, arithmetic/linear method, geometric method, exponential method, matrix method, etc., need of population projections.
Stable and stationary population, their characteristics and uses, Lotka’s characteristics equation, intrinsic birth and death rates, effect of uniform drop in force of mortality on the growth rate, effects of changes in fertility and mortality on the age distribution of population. Model life tables, Coale and Demeney regional model life tables.
Population in Bangladesh: History of growth of population in Bangladesh; Implications of the growth of population in Bangladesh; Population policy in Bangladesh; Level, trends and determinants in fertility, mortality and migration in Bangladesh; Interrelationship between population and development; Future prospects of population and population control in Bangladesh; Aged and aging of population in Bangladesh

Credits 3
Pre-requisite AST-205

AST- 307
Description

National income: Concepts, Measurement and Problems; Social Accounting Matrix. Income Distribution and Wealth: Causes of Concentration; Meaning of Inequality; Measures of Inequality; Frequency of Income; Lorenz Curve of Income; Gini coefficient; Atkinson’s index, etc.
Poverty: Conceptual issues of Poverty; Measurement of Different Poverty Indices.
Introduction to Psychometrics: Measurement in Psychology and Education; Intelligent and Achievement tests; Test scores; Equivalence of Scores; Z-score and T-score; Intelligent Quotient.
Definition, Nature and Importance of Anthropology; Role and Functions of Family
Social inequality: Inequality by Sex, Age, Rank, Caste, Race, Class, Power, Rule and Social Connections.
Social Sector Development Policies: Development in Agriculture, Industry (a) Growth Performance, Outlay and Yield (b) Agrarian Structure and Its changes (c) Plan Outlay; Rural Development; Human Development; Women and Youth Development; Land Reforms in Bangladesh; InfrAST-ructure Development; ADP allocation to social sectors; Fiscal Policies for Development.

Credits 3
Pre-requisite AST-205

AST- 308
Description

  • Brief knowledge in SPSS
  • Creating a data file in SPSS
  • Data Manipulation: Inserting variables, Inserting case, Merging files, case selection, selecting a random sample, aggregate data, splitting file, weight cases
  • Data Transformation
  • Categorize variables
  • Frequency distribution table
  • Measures of central tendency, measures of dispersion
  • Creating graphs and cross tables
  • Test of hypothesis
  • Correlation and regression

SAS Programming

  • Introduction to SAS
  • SAS Syntax
  • SAS Datasets
  • Reading SAS Datasets
  • Reading Delimited Raw Data
  • Manipulating Data
  • Validating and Cleaning Data
  • Combining SAS Data Sets
  • Compilation and Execution of the Data Step
  • Producing Summary Reports
  • Enhancing Reports
  • Basics of ODS
  • Processing Data Iteratively
  • Transforming variables
  • Basic Statistics Using SAS
  • Univariate Description and Inference
  • ProcUnivariate
  • Analysis of Variance
  • Categorical Data Analysis
  • Linear Regression
  • Logistic Regression
Credits 3
Pre-requisite AST-203, AST-204, AST-304

AST- 309
Description

  • Review of elementary probability contents
  • Foundational comparison of parametric and nonparametric approaches
  • Dichotomous data problem
  • General connection between confidence sets and hypothesis tests
  • General connection between point estimates and hypothesis tests
  • Goodness-of-fit Tests (Kolmogorov-Smirnov two-sample test for general differences, Run test)
  • Tests for a single location parameter
  • Test for several location parameters
  • Tests for scale parameters
  • Distribution tests
  • Measures of Association
  • Tests for Randomness trends
  • Nonparametric regression
  • Sign test and associated interval and point estimates for one-sample data
  • Signed rank test, interval and point estimates for one-sample data
  • Rank Correlation
  • Wilcoxon signed rank test
  • Wilcoxon sum rank test
  • Mann-Whitney U test
  • Kruskal-Wallis test
  • Asymptotic relative efficiency comparisons
  • Rank sum test, interval and point estimates for two-sample data
  • One-Way Layout: tests and multiple comparison procedures
  • Two-Way Layout: tests and multiple comparison procedures
  • Kendall’s tau procedures for independence of two random variables
Credits 3
Pre-requisite AST-303

Description

AST- 310

Introduction: Distributions and Inference for Categorical Data
Categorical Response Data; Distributions for Categorical Data; Statistical Inference for Categorical Data
Describing Contingency Tables
Probability Structure for Contingency Tables; Comparing Two Proportions; Partial Association in Stratified 2×2 Tables; Extensions for I×J Tables

Inference for Contingency Tables
Confidence Intervals for Association Parameters; Testing Independence in Two-Way Contingency Tables; Following-Up Chi-Square Tests; Two-Way Tables with Ordered Classifications.
Introduction to Generalized Linear Models
Generalized Linear Models for Binary Data and counts; Moments and Likelihood for Generalized Linear Models; Inference for Generalized Linear Models; Fitting Generalized Linear Models; Quasi-likelihood and Generalized Linear Models
Logistic Regression
Inference and Interpreting Parameters in Logistic Regression; Logit Models with Categorical Predictors; Fitting Logistic Regression Models

Credits 3
Pre-requisite MAT102, MAT206, AST-201

AST- 401
Description

  • Modern probability: probability as a set function; Borelfield and extension of probability measure
  • Probability measure notion of random variables; probability space; distribution function; expectations and moments
  • Convergence of random variables; Laplace transformation
  • Markov Chains: introduction, transition probability matrices of a Markov chain, First step analysis; some special Markov chains; Regular transition probability matrices
  • The classification of states; Basic limit theorem of Markov chain; Reducible Markov chains
  • Poisson process: the Poisson distribution, counting and Poisson process; the law of rare events
  • Continuous time Markov chains: pure birth processes; pure death processes; birth and death processes
  • Limiting behavior of birth and death processes; birth and death process with absorbing states; finite state continuous time Markov chains
  • Renewal theory and its applications : introduction, distribution of N(t), limit theorems and their applications
  • Renewal reward process regenerative process, semi Markov process, queing process
  • The connection between Poisson process and the Poisson distribution, Poisson process as
  1. the distribution of waiting between events
  2. the distribution of process increments

iii. the behavior of the process over an infinitesimal time interval

Credits 3
Pre-requisite NONE

AST- 402
Description

Introduction to Research: What is Research? Research Concepts, Concept, aims and objectives of research; types of research, steps involved in research, selection and formulation of research problems; proposal writing; examining the designs ofsome known researches
Questionnaire: Questionnaire, check lists, FGD guidelines etc.; preparation of questionnaires. Preparation of manuals for interviewer, Enumerators training, monitoring and supervision for controlling the quality of data; how to avoid non-response
Report writing: Report writing; content and organizations of the report; heading and subheadings; techniques of writing conclusion, summary, recommendations, footnotes references, appendix, Examining some local and international reports
The concept of monitoring and evaluation (M & E): Objectives, usefulness and scope of M & E. Views of different schools on M & E. Performance monitoring versus performance evaluation
Timing and type of M & E: Summative, formative, continuous, participatory, diagnostic, log frame, etc.; baseline, ongoing and end line evaluation; impact evaluation; M & E of ongoing programs (activities, inputs, outputs, effect); follow-up for remedies, and post programs evaluation
Monitoring and evaluation plan and data sources: Indicators for monitoring and evaluation, Identification of indicators and characteristics of ideal indicators; factors influencing indicator selection
Quantitative Research Methods: The Scientific Method, Design of Quantitative Surveys, Quantitative Research Methods—Wrap-Up
Qualitative Research: Introduction to Qualitative Research and Research Approaches, Qualitative Research Methods—The Toolkit, Data Analysis and Theory in Qualitative Research Articles
Reliability and Validity in Measurements: Initiation of model building, Measurement error, Test for sound measurement, Reliability and its measurements, Validity and its types, Measurements of validity; stability of the model over the population, Construction of measurements scales
Field trip, report writing and presentation on selected topics

Credits 4
Pre-requisite AST-302, AST-306

AST- 403
Description

  • Preliminaries of multivariate analysis: applications of multivariate techniques
  • The organization of data; data display and pictorial representations; distance
  • Random vectors and random sampling: some basic of matrix and vector algebra; positive Definite matrices; a square-root matrix; random vectors and matrices; mean vectors and covariance matrices; matrix inequalities and maximization
  • The multivariate normal distribution: the multivariate normal density and its properties
  • The multivariate marginal, conditional and joint probability distributions
  • Assessing the assumption of normality; detecting outliers and data cleaning; transformation to near normality
  • Inferences about a mean vector: the plausibility of mean vector as a value for a normal population mean; Hotelling T and likelihood ratio tests; confidence regions and simultaneous comparisons of component means
  • Large sample inference about a population mean vector; inferences about mean vectors when some observations are missing; time dependence in multivariate data
  • Comparisons of several multivariate means: paired comparisons and a repeated measures design; comparing mean vectors from two populations
  • Principal components: Introduction and concepts of principal components
  • Factor analysis: Introduction, The orthogonal factor model and methods of estimation
  • Canonical correlation analysis: Introduction and basic concepts
  • Discrimination and Classification: Introduction, separation and classification for two populations
  • Profiles analysis; repeated measures designs and growth curves
Credits 3
Pre-requisite MAT101, MAT206, AST-201, AST-303

AST- 404
Description

Basic Concepts & Models:
Introduction, lifetime distribution, continuous model, discrete model, hazard function, exponential distribution, Weibull distribution, log-normal distribution, log-logistic distribution, gamma distribution, regression models
Observation schemes, Censoring & Likelihood:
Types of censoring and maximum likelihood, Truncation
Some Nonparametric & Graphical Procedures:
Nonparametric estimation of a survivor function and quantiles, Non parametric methods for estimating survival function and variance of the estimator viz. Acturial and Kaplan- Meier methods product limit estimate, Nelson-Aalen estimate, plots involving survivor or cumulative hazard function, estimation of hazard or density function, methods for truncated and interval censored data, life tables
Inference Procedure for Parametric Models:
Inference procedure for exponential distribution, for gamma distribution, models with polynomial based hazard function, grouped, interval censored or truncated data
Parametric regression models:
Log-location scale regression model, proportional hazard regression model

Credits 3
Pre-requisite AST-201, AST-304, AST-305, AST-309

AST- 405
Description
Industrial Statistics: Fundamental concepts of industrial statistics, its purposes and real life application; industrial quality control.Total quality control; statistical quality control; chance and assignable causes of variation; statistical process control.
Control chart: concept of control chart; necessary steps for constructing control charts; types of control charts; p-chart; d-chart; c-chart; u-chart; R and S charts (control charts with standard given and control charts with no standard given);
Basic concepts of acceptance sampling; OC curve and its uses; types of OC curves; properties of OC curves.
Basic concepts of single sampling plan for attributes; constructed of type A and type B OC curves under the single sampling plan for attributes; specific points on the OC curve (AQL, LTPD); rectifying inspection; AOQ; AOQL; ATI; ASN; designing a single sampling plan;
Basic concepts of double sampling plan; introduction to multiple sampling plan and sequential sampling analysis;
Operations Research: Nature and impact of OR approach; phases of OR. Concept of linear programming problem (LPP); construction of LPP; Solution of LPP: graphical and the simplex method; revised simplex method; Big-M method, two phase method; concept of convergence, degeneracy and cycling.
Duality: dual primal relationship and formulation of dual problems.
Sensitivity analysis: introduction to sensitivity analysis.
Game theory: finite and infinite games; zero sum games; two person zero sum games; pay off matrix; maximum and minimum criterion of optimal solution of a game; dominance property;

Credits 3
Pre-requisite MAT101, AST-201

AST- 406
Description
Introduction:
Examples of time series, Objectives, Types of variation, Stationarity, Trends and Seasonal Components, No Seasonal Component, Trend and Seasonality, time plot
The autocovariance of a stationary time series:
Strict stationarity, applied to stationary time series, drawbacks of shift operator, backwards difference, the spectral density, Time series models, Box-Jenkins Model, concept of a filter, root characteristic equation of time series
Estimation of the mean and the autocovariance:
Estimation of Mean, Estimation autocovariance, Prediction, A short course in inference, Prediction of random variables, Prediction for stationary time series
The Wold decomposition and Partial correlation:
Partial autocorrelation, AR process, MA process, ARMA processes, Calculation of the ACVF, Prediction of an ARMA Process, conintegrated time series, ARIMA time series
Random Walk:
Concept and properties of discrete random walks and random walks with normally distributed increments, both with and without drift
Multivariate Autoregressive Model: Concept
Spectral analysis:
The spectral distribution, Spectral representation of a time series, Prediction in the frequency domain, Interpolation and detection, Estimation of the spectral density, the periodogram, Smoothing the periodogram, Linear filters
Forecasting:
Introduction, univariate procedures, multivariate procedures, comparative review of forecAST-ing procedures, prediction theory
Identification, Estimation and Diagnosis of a time series:
Criteria for choosing between models, diagnostic tests applied to residuals
Text: Makridakis, S., Wheelwright, C. and Hyndman, R.J. (1997). ForecAST-ing Methods and Application, 3rd Edition. Wiley

Credits 3
Pre-requisite AST-303, AST-304

AST- 407
Description
Generalized linear models: Exponential family of distributions; Properties of distributions in Exponential family,Component of GLM, Random systematic link function
Estimation: method of maximum likelihood, method of Least- squares, estimation of generalized linear models
Inference: sampling distribution for scores, sampling distribution for maximum likelihood estimators,
Confidence intervals for model parameters, adequacy of a model, sampling distribution for log-likelihood statistic, log-likelihood ratio statistic (deviance),assessing goodness of fit, hypothesis testing;
Multiple Regression: maximum likelihood estimation, log-likelihood ratio statistic;
Models for binary responses: probability distributions, generalized linear models, general logistic regression, maximum likelihood estimation and log-likelihood ratio statistic, other criteria for goodness of fit, leAST- square methods; Multinomial distributions; Nominal logistic regression models; Ordinal logistic regression models;
Models for count Data: probability distributions, log-linear models, maximum likelihood estimation,
Hypothesis testing and goodness of fit

Credits 3
Pre-requisite AST-303, AST-304

AST- 408
Description

Introduction to Life insurance: life insurance and annuity contracts, pension benefits, mutual and proprietary insurers
Survival Models: Actuarial notation, future lifetime random variable, force of mortality, curtate future lifetime
Life tables and Selection: Life tables, fractional age assumptions, national life tables, survival models for life insurance policy holders, mortality trends
Insurance Benefits: assumptions, valuation of insurance benefits
Annuities: Annual annuities, annuities payable continuously, increasing annuities, evaluating annuity functions
Premiums: Preliminaries, assumptions, future loss random variable, the equivalence principle
Policy Values: Policy with annual cash flows, policy with continuous cash flows, policy alterations
Multiple State Models: Alive Dead Model, Permanent disability model, the disability income insurance model, Markov multiple state models in discrete time,
Joint Life and last Survivor benefits: Joint life and last survivor benefits, a multiple state model for independent future lifetimes, a model with dependent future lifetimes, the common shock model.

Credits 3
Pre-requisite AST-201, AST-303, AST-305

AST- 409
Description

Bayesian Inference:
Bayes theorem; prior ignorance; likelihood; odds ratio; Bayes factor; Bayesian inference for discrete random variable; Bayes theorem for binomial distribution with discrete prior;
Bayesian inference for continuous random variable; Bayesian inference for normal mean; Bayesian inference for difference between means; Comparing Bayesian and frequentist inference for proportion, for mean

Decision Theory:
Fundamental concept of decision theory; action space; Bayes decision rule and related examples, Role of sufficient statistics; James-Stein estimator; Minimax rule

Robust statistics:
The meaning of robustness, deviations from parametric models and estimation theory; Inuence function (IF), gross-error sensitivity, local-shift sensitivity, rejection point, asymptotic variance, breakdown point, identification of outliers; Definitions of M-, L-, and R-estimators

Credits 3
Pre-requisite AST-303, AST-304

AST- 410
Description
• The Basics of Working with Stata: Starting a Sample Stata Session, Different Type of Files in Stata, Useful Commands in Stata, Overview of Stata Syntax
• Importing and Exporting Data in Stata: Using and Saving Stata Data Files, Inputting Raw Data, Inputting Data from Spreadsheets, Inputting Data from Other Statistical Programs, Inputting Data from Fixed-Format Text Files
• Basic Data Management in Stata: Labeling Data, Variables and Values, Creating and Recoding Variables, Subsetting Variables and Observations, Collapsing Data Across Observations, Working Across Variables, Combining Stata Data Files : Append and Merge, Reshaping Data from Wide to Long, Reshaping Data from Long to Wide
• Graphics: Introduction to Graphics, Overview of Graph Two-way Plots, Two-way Scatter plots, Combining Two-way Scatter plots, Common Graph Options
• Summary Statistics and Tables: Summary Statistics for Measurement Variables, Frequency Tables and Two-Way Cross-Tabulations, Multiple Tables and Multi-Way Cross-Tabulations, Tables of Means, Medians, and Other Summary Statistics
• ANOVA and Other Comparison Methods: One-Sample Tests, Two-Sample Tests, Analysis of Variance (ANOVA)
• Linear Regression Models: Correlation and Regression, Multiple Linear Regression, Predicted Values and Residuals, Basic Graphs for Regression, Hypothesis Tests, Dummy Variables, Automatic Categorical Variable Indicators and Interactions, Diagnostic Plots
• Models for Binary and Categorical Outcomes: Logistic Regression, Probit Regression
• Count Models: Poisson Regression, Negative Binomial Regression
• Principal Components, Factor, and Cluster Analysis: Principal Components, Factor Analysis, Cluster Analysis
• Time-series with Stata: Smoothing, Time Plot, Lag, Leads, Differences, Correlograms, Introductory Time Series Models
• Structural Equation Modeling: Introduction to SEMs, Major types of SEMs, General SEM in Stata

Credits 3
Pre-requisite AST-303, AST-304

AST- 499
Description

Each student will be required to prepare a project report and present the report in a seminar. For the project work, each student will be assigned to a teacher at the beginning of the academic year. Submission and evaluation should be made before the commencement of final examination. Fifty percent weight of the course will be allotted to project works and the remaining fifty percent for seminar presentation.
The internal members of the examination committee will evaluate the performance in the seminars and the report will be evaluated by one internal examiner and one external examiner nominated by the examination committee.

Credits 3
Pre-requisite NONE

Description

Credit-3

  • Sampling and Sampling Distributions.
  • Expectations of functions of random variables: expectation two ways, sums of random variables, product and quotient;
  • Independence of random variables, mean and variance of linear combinations of random variables
  • Deriving distributions of the linear combinations of random variables
  • Cumulative distribution function technique: distribution of minimum and maximum, distribution of sum of difference of two random variables, distribution of product and quotient;
  • Moment generating function technique: description of technique, distribution of sums of independent random variables; The transformation Y = g(X): distribution of Y = g(X), probability integral transformation;
  • Transformations: discrete random variables, continuous random variables;
  • Sampling: basic concepts of random samples, inductive inference, populations and samples, distribution of samples, statistic and sample moments; Sample mean: mean and variance
  • Central limit theorem, normal approximations to other distributions, continuity correction
  • law of large numbers, central limit theorem, Bernoulli and Poisson distribution, exponential distribution, uniform distribution, Cauchy distribution;
  • Sampling from the normal distributions: role of normal distribution in statistics, samples mean, chi-square distribution, the F-distribution, Student’s t-distribution.
  • Non-central distributions: non-central chi-squared, t, and F distributions; definitions, derivations, properties
Credits 3
Pre-requisite AST-101, AST-102
+ Master of Science in Actuarial Science

ASTA 501
Description

  • The Concept of Actuarial Science: The basics and nature of actuarial science, coverage, examples
  • The Concept of Insurance: The basics and nature of insurance – evolution and nature of insurance, functions of insurer, financial aspects of insurer operations
  • Risk Management: Provides an understanding of risk management, different types of risks, actual and consequential losses, management of risks, loss minimization techniques.
  • The Business of Insurance: Management of risk by individuals, management of risk by insurers, fixing of premiums, reinsurance and its importance for insurers, role of insurance in economic development and social security, contribution of insurance to the society.
  • The Insurance Market and Customers: The various constituents of the insurance market, Understanding insurance customers, importance of ethical behavior.
  • Insurance Terminology: Common terms used in insurance – terms common to both life and non – life insurance – terms are specific to life and non – life insurance – how insurance terms are used.
  • Life Insurance: Introduction to Life Insurance, the Actuarial Basis of Life Insurance different products offered by life insurers, term plans, pure endowment plans, combinations of plans, traditional products, linked policies, features of annuities and group policies, , Premiums and Bonuses, employee Benefits and Other business uses of Life Insurance, Group Insurance, Linked Insurance, Policy documents, premium pays, policy lapse, revival, assignment, nomination and surrender of policy, policy claims
  • General Insurance: Risks faced by the owner of assets, policy documents & forms, general insurance products, underwritings, ratings and premium, claims, reserves and accounting.
  • Health Insurance: Introduction to health insurance: basics and applications
  • Insurance Law: Development of Insurance Legislation in Bangladesh and Insurance Act 1938, Regulations of Insurance industry, the legal framework, IDRA functions and other regulatory authorities, Policy Holders Rights of Assignment, Nomination and Transfer, Protection of Policy Holders Interest, Dispute Resolution Mechanism, Financial Regulatory aspects of Solvency margin and Investments, International Trends In Insurance Regulation
  • Insurance Rules and Acts:The Insurance Rules 1958,The Insurance Act 2010,Insurance Development and Regulatory Authority Act 2010,Insurance Corporation Act 1973,Rules and Regulations made under the Insurance Act 2010.

Text Book: Jones, H. E., Long, D. L. Principles of insurance: Life, health, and annuities, 2nd edition. FLMI Insurance Education Program, Life Management Institute LOMA, 1999

Reference

  1. Vaughan, E. J., Vaughan, T. M. Fundamentals of Risk and Insurance, 10th Edition. Barnes & Noble, 1972.
  2. The Insurance Act: 1938, Legislative and Parliamentary Affairs Division, Ministry of Law, Justice and Parliamentary Affairs.
  3. Mehr, R, Cammack,E  and Rose,T. Principles of Insurance.8 Sub Edition.Irwin Series in Insurance and Economic Security, 2013.
  4. Jerry II, R. H. and Richmond, D.S. Understanding Insurance Law, 5th Edition Lexis Nexis, 2012.
Credits 3
Pre-requisite

ASTA 502
Description

  • Cash flow model of financial transactions: For a given cash flow process, determination of inflows and outflows in each future time period considering certainty and uncertainty.
  • Concepts of compound interest and discounting: Accumulation of single investment, defining present value of future payment, discounting at fixed/variable interest rate.
  • Interest or discount rates in terms of different time periods: Relationship between the rates of interest and discount over various time periods, deriving relationship between rates of interest payable once per effective period and the rate of interest payable p times per unit time period, difference between nominal and effective rates of interest.
  • Concepts of real and money interest rates: Calculating present value and accumulated value of a stream of equal or unequal payments using specified rates of interest and the net present value at a real rate of interest, calculating the present value and accumulated value of a series of equal or unequal payments made at regular intervals under the operation of specified rates of interest considering immediate and deferred payment.
  • Annuities and accumulation: Deriving formulas for annuity due, annuity payable in arrear, deferred annuity, accumulated value payable in arrear or due, perpetuity.
  • Definition of an equation of value: Defining an equation of value for certain or uncertain payments.
  • Loan scheduling: Describing flat rates and effective rates, calculating schedule of repayments under a loan and identifying interest or capital components of any repayment.
  • Discounted cash-flow techniques: Calculating net present value and accumulated profit of the receipts and payments from an investment project at given rates of interest, Calculating the internal rate of return implied by the receipts and payments from an investment project, describing and determining payback period and discounted payback period implied by the receipts and payments from an investment project, calculating money-weighted rate of return, time-weighted rate of return and linked internal rate of return on an investment or a fund.
  • Investment and risk characteristics: Describing investment and risk characteristics of fixed-interest government borrowings, fixed-interest borrowings by other bodies, index-linked government borrowings, shares and other equity type finance, derivatives.
  • Analysis of elementary compound interest problems: Calculating the present value of payments from a fixed interest security where the coupon rate is constant and the security is redeemed in one instalment, calculating upper and lower bounds for the present value of a fixed interest security that is redeemable on a single date within a given range at the option of a borrower, calculating the running yield and the redemption yield from a fixed interest security, calculating the present value or yield from an ordinary share and a property, calculating the present value or yield from an index-linked bond, calculating the price of, or yield from,  a fixed-interest security considering income tax and capital gain tax.
  • Arbitrage free pricing methods: Calculating the price of forward contracts, explaining ‘hedging’ in the case of forward contract, calculating the value of a forward contract at any time during the term of the contract in the absence of arbitrage.
  • Term structure of interest rates: Factors influencing the term structure of interest rates, explaining par yield and yield to maturity, discrete spot rates and forward rates, continuous spot rates and forward rates, defining the duration and convexity of a cashflow sequence, Redington’s theory for immunization of a portfolio of liabilities.
  • Simple stochastic models for investment returns: Describing the concept of a stochastic interest rate model and the fundamental distinction between stochastic and deterministic model.

Text Book

  1. McCutcheon, J.J. Scott W.F (2003). An Introduction to the Mathematics of Finance. Butterworth-Heineman.
  2. Sohrab Uddin M. (1992). An Introduction to Actuarial and Financial Mathematics, Bangladesh.

References

  1. Kellison S.G., (1991). The Theory of Interest. 2nd Irwin.
  2. Garrett, S. J. (2013). An Introduction to the Mathematics of Finance: A Deterministic Approach. 2nd Butterworth-Heinemann.
  3. Newton, L. Bowers, Hans, U. Gerber, James, C. Hickman, Donald, A. Jones, Cecil, J. Nesbitt (1997). Actuarial mathematics. 2nd Edition. Society of Actuaries.
Credits 3
Pre-requisite

ASTA 503
Description

  • Statistics and its origin
    Definition, uses & importance, population & sample, sources of statistical data, parameter and statistic.
  • Summarizing Data
    Data, Levels of Measurements, variable and attribute, summarizing and presenting data, frequency distribution, graphs and diagrams
  • Measures of Central Tendency
    Arithmetic mean, median, quartiles, percentiles, deciles, mode, geometric mean, and harmonic mean
  • Measures of Dispersion
    Variance, mean deviation, standard deviation, and other measures of dispersion, moments, shape characteristics of a distribution, box and whisker plots
  • Simple Linear Regression and Correlation
    Measures of correlation, rank correlation, scatter diagram, simple linear regression, assumption, least square method, properties of regression coefficient, partitioning the total variation in regression, coefficient of multiple determination
  • Probability
    Meaning, definition, scope, set theory, sample space, elements of set theory; axiomatic definition of probability, permutation and combination, conditional probability and rules of probability for dependent and independence cases, and Bayes theorem;
  • Probability function and mathematical expectation
    Random variables, probability density function, distribution function; joint marginal and conditional distributions; mathematical expectation, expectations of sums and products of random variables; variance, conditional expectation and variance.
  • Discrete Probability Distributions
    Bernoulli, binomial, Poisson, geometric, negative binomial, hypergeometric, and uniform distributions
  • Continuous Probability Distributions
    Uniform, exponential, gamma, beta, normal, log- normal, and Weibull distributions
  • Generating Functions
    Identification of Moment and Cumulant generating functions, characteristic function of discrete and continuous distributions; determination of probability generating function of discrete and integer-valued random variables
  • Sampling Distribution
    Basic concepts of random samples, sampling and sampling distribution, expectations of functions of random variables: sums of random variables, product and quotient; independence of random variables, mean and variance of linear combinations of random variables
  • Distributions of the linear combinations of random variables: cumulative distribution function technique, moment generating function technique, transformations technique
  • Law of large numbers, central limit theorem, standard normal distribution, chi-square distribution, F-distribution, t-distribution,
  • Cauchy-Schwartz, Markov and Chebyshev’s inequality

Text Book

  1. Rohatgi V.K. and Saleh A.K.M. (2000). An Introduction to Probability and Statistics. 2nd Edition. A Wiley-Interscience Publication.
  2. Mostafa M.G. (1989). Methods of Statistics. Dhaka: Karim Press & Publication.

References:

  1. Daniel W. (2009). Biostatistics: Basic Concepts and Methodology for the Health Science. 9th WSE.
  2. Bulmer M .G. (1967). Principles of Statistics. 2nd Oliver and Boyd, Edinburgh.
  3. Ross S. (2012). A First course in Probability. 9th Pearson Prentice Hall, NJ.
  4. Mood A.M., Graybill F.A. and Boes D.C. (1974). Introduction to the Theory of Statistics. 3rd McGraw-Hill.
  5. Meyer P.L. (1970). Introductory Probability and Statistical Applications. Addison-Wesley, USA.
  6. Islam, M.N. (2004). An Introduction to Statistics and Probability. 3rd Mullick Brothers.
  7. Roy, M.K. (2001). Fundamentals of Probability and Probability Distributions. 3rd Romax Publications.
  8. Ross S.M (1988). A First course in Probability. 3rd edition. Macmillan.

 

Credits 3
Pre-requisite

ASTA 504
Description

  • Methods of finding estimators: methods of moments, maximum likelihood, and other methods
  • Properties of point estimators: closeness, mean-squared error, loss and risk functions
  • Sufficiency: sufficient statistics, factorization criterion, minimal sufficient statistics, ancillary statistics
  • Completeness: complete statistics, exponential family
  • Parameter Estimation: point estimates of mean, proportion, and variance. Confidence intervals for parameters: mean, proportion, and variance. Large sample properties and procedures
  • Test of hypothesis: simple hypothesis & composite hypothesis, critical region, best critical region, Neyman-Pearson fundamental lemma, most powerful tests, uniformly most powerful critical region, UMP tests. Hypothesis testes for mean, proportion, and variance
  • NonParametric Tests: Goodness-of-fit tests (Kolmogorov-Smirnov two-sample test for general differences, Run test) , Sign test and associated interval and point estimates for one-sample data, Signed rank test, interval and point estimates for one-sample data, Wilcoxon signed rank test, Wilcoxon sum rank test, Mann-Whitney U test, Kruskal-Wallis test, Asymptotic relative efficiency comparisons, Rank sum test, interval and point estimates for two-sample data, Two-Way Layout: tests and multiple comparison procedures, Kendall’s tau procedures for independence of two random variables
  • Bayesian Inference: Bayes theorem; prior ignorance; likelihood ratio; Bayes factor; Bayesian inference for discrete random variable; Bayes theorem for binomial distribution with discrete prior; Bayesian inference for continuous random variable; Bayesian inference for normal mean; Bayesian inference for difference between means; Comparing Bayesian and frequentist inference for proportion and mean, Loss function, Risk functions, related problems
  • Design of Experiments
    Complete Randomize Design (CRD), Randomized Block Design (RBD), Latin Squares Design (LSD), estimating model parameters; example of real life application of these experiments; comparisons among treatment means, contrasts, orthogonal contrasts, Scheffe’s method, comparing pairs of treatment means, The two-factor factorial design; statistical analysis of fixed effects, random effects, and mixed effects models; Analysis of Covariance; Description of the procedure; Factorial experiments with covariates.

Text Book

  1. Casella, G. and Berger, R.L.O. (2002). Statistical Inference. 2nd Edition. Duxbury, New York.
  2. Montogomery, D.C. (2001). Design and Analysis of Experiments. 5th John Wiley and Sons Inc.

References

  1. Johnson, N.L, Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions. Vol. 1.  2nd Edition. John Wiley, New York.
  1. Hogg, RV and Craig, AT (2012). Introduction to Mathematical Statistics. 7th Pearson.
  2. Mood, A.M., Graybill, F.A. and Boes. D.C. (1974). Introduction to the Theory of Statistics. 3rd McGraw-Hill.
  3. Kvam, P.H. and Vidakovic B. (2007). Nonparametric Statistics with Applications to Science and Engineering.
  4. Sprent, P. and Smeeton, N.C. (2001). Applied Nonparametric Statistical Methods.3rd Chapman & Hall/CRC.
  1. Kendall, M., Stuart, A. and Ord, J.K. (1998). Kendall’s Advanced Theory of Statistics, Distribution Theory. Vol 1. 6th Edition. Oxford University Press, USA.
  2. Kendall, M., Stuart, A. and Ord, J.K. (1999). Kendall’s Advanced Theory of Statistics, Classical Inference and the Linear Model. Vol 2A. 6th Edition. Oxford University Press, USA.
  3. O’ Hagan A. (1994). Kendall’s Advanced Theory of Statistics, Vol 2B: Bayesian Inference. Edward Arnold.
  4. Cox, D.R. & Hinkley, D.V. (1974). Theoretical Statistics. 2nd Edition. Chapman and Hall, London.
  5. Hoel, P.G. (1984). Introduction to Mathematical Statistics. 5th Ed. Wiley, NY.
  1. Bolstad, W.M. (2007). Introduction to Bayesian Statistics.2nd Wiley.
  2. Lee, P .M. (2004). Bayesian Statistics: An Introduction.3rd Wiley.
  3. Kirk,R.E. (2012): Experimental Design. 4th Edition. SAGE Publications, Inc.

 

Credits 3
Pre-requisite

ASTA 505
Description

  • Simple Linear Regression Model
    Least squares estimation, estimation of variance, inferences, interval estimation, prediction, Analysis of Variance, R-square, residual analyses, transformations as solution to problems with the model
  • Multiple Regression Models
    Basic estimation and inference for multiple regression, Generalized Least Squares and Weighted Least Squares, Extra Sum of Squares Principles and related tests; multicolliniarity, autocorrelation, model diagnostics and selecting the best regression equations
  • Generalized linear models: exponential family of distributions; Properties of distributions in Exponential family, Component of GLM, Random systematic link function; method of maximum likelihood, method of least squares estimation of generalized linear models; Scores and information matrices; confidence intervals for model parameters, adequacy of a model, log-likelihood ratio statistic (deviance), assessing goodness of fit, hypothesis testing
  • Models for binary responses: generalized linear models,  general logistic regression, maximum likelihood estimation and log-likelihood ratio statistic, other criteria for goodness of fit, least square methods; multinomial distributions; ordinal logistic regression models
  • Models for count Data: log-linear models, maximum likelihood estimation, hypothesis testing and goodness of fit

Reference 

  1. Draper, N.R. and Smith, H. (1999). Applied regression analysis. 3rd Wiley.
  2. Kutner, M., Nachtsheim, C. and Neter, J. (2004). Applied Linear Regression Models. 4th McGraw Hill/Irwin Series.
  3. Chatterjee, S. and Hadi, A.S. (2012). Regression Analysis by Example. John Wiley, NY.
  4. Graybill, F.A. (1961). An Introduction to Linear Statistical Models. Vol-1. McGraw Hill, NY.
  5. Montogomery, D.C, Peck, E. and Vining, G.G. (2007). An Introduction to Linear Regression Analysis. 4th Edition. John Wiley, NY.

 

Credits 3
Pre-requisite

ASTA 506
Description

  • Investment and asset management: Principal terms in use
  • Key principles of finance: Relationship between finance, real resources, and objectives of an organization, relationship between the stakeholders in an organization (including lenders and investors), the role and effects of the capital markets, agency theory, the theory of the maximization of shareholder wealth
  • Forms of Business Organization: Characteristics of sole traders, partnerships and limited companies as business entities, different types of loan and share capital, public and private company, and limited company
  • Company finance: Medium Term Company Finance, hire purchase, credit sale, leasing, bank loans, Short term Company Finance: bank overdrafts, trade credit, factoring, bills of exchange, commercial paper
  • Principles of personal and corporate taxation: Basic principles of personal taxation, basic principles of the taxation of capital gains, basic principles of company taxation, different systems of company taxation from the points of view of an individual shareholder and the company, basic principles of double taxation relief
  • Principal forms of financial instrument: Methods for seeking a quotation on stock exchange and seeking a quotation for securities debenture stocks, unsecured loan stocks, Eurobonds, preference shares, ordinary shares, convertible unsecured loan stocks, convertible preference shares, warrants, floating rate notes, subordinated debt, options issued by companies, issues of securities, scrip issue, rights issue, financial futures, options, interest rates, currency swaps
  • Capital Structure and Dividend policy: Capital structure, financing and valuation, market valuation, dividend policy, distribution of profits
  • Capital Budgeting and Risk Management: Introduction to Risk and Return, Portfolio Theory and the Capital Asset, Pricing Model, Risk and the Cost of Capital, Managing Risk, Project Analysis, Investment, Strategy, and Economic Rents, Agency Problems, Compensation, and Performance Measurement, Working Capital Management
  • Financial institutions: Central banks, investment exchanges, investment banks, clearing banks, building societies, investment trusts, unit trusts, investment management companies, self-administered pension funds, life insurance companies, general insurance companies
  • Role and Principal Features of Accounts of a Company: Introduction to financial statements, key accounting treatments, Introduction to management accounting and relevant costs for decisions, Costing, Budgeting and budgetary control, interpretation of reports and company accounts, contents and features of insurance company accounts
  • Insurance Rules 1958, Insurance Rules and Regulations made under the Insurance Act 2010 and Insurance Development and Regulatory Authority Act 2010

References:

  1. Atrill, P., McLaney, E. Accounting and finance for non-specialists. 9th ed. Prentice Hall, 2015.
  2. Brigham, E. F., Houston, J. F. Fundamentals of financial management (concise edition). 7th ed. South-Western, 2011.
  3. Davidson, A. How to understand the financial pages. 2nd ed. Kogan Page, 2008.
  4. Holmes, G., Sugden, A., Gee, P. Interpreting company reports and accounts. 10th ed. Prentice Hall, 2008
  5. Brealey, R. A., Myers, S. C., Allen, F Principles of corporate finance (Global edition). 11th ed. McGraw-Hill, 2014.
Credits 3
Pre-requisite

ASTA 507
Description

  • Introduction: Basic concept of demography; sources of demographic data: census, vital registration system, sample surveys, and population register types of errors and methods of testing the accuracy of demographic data.
  • Population growth: Components, techniques to measure it, doubling time, population estimates and projections, different techniques of population projection-component method, arithmetic/linear method, geometric method, exponential method etc. need of population projections. Gompartz & Makehaum curves, Logistic curve
  • Fertility and Mortality: measures of fertility, crude birth rate, age specific fertility rates, general fertility rate, total fertility rate, gross reproduction rate and net reproduction rate; measures of mortality; crude death rate, age specific death rates, infant mortality rate, child mortality rate, neo-natal mortality rate, standardized death rate its need and use, sex ratio, dependency ratio, density of population.
  • Life Table: Concept, structure and calculation; complete and abridged life table, different life table functions and inter-relationships among them, use of life table, Actuarial life table, competing risk life table, multiple decrement life table.
  • Force of Mortality: Idea and definition calculation of life table with the help of force of mortality, stable and stationary population, their characteristics and uses, Lotka’s characteristics equation, intrinsic birth and death rates
  • Parametric Regression Models: Inference procedure for exponential distribution, for gamma distribution, models with polynomial based hazard function, interval censored or truncated data, log-location scale regression model, proportional hazard regression model, graphical methods for model selection, inference for log-location scale models, and extension of log-location scale models
  • Nonparametric & Graphical Procedures: Nonparametric estimation of a survivor function and quintiles, actuarial and Kaplan-Meier methods, Nelson-Aalen estimate, plots involving survivor or cumulative hazard function, estimation of hazard or density function, methods for truncated and interval censored data
  • Censoring & Likelihood: Types of censoring and maximum likelihood, truncation
  • Survival Analysis: Basic concepts, lifetime distribution, continuous model, discrete model, hazard function, exponential distribution, Weibull distribution, log-normal distribution, log-logistic distribution, gamma distribution, regression models
  • Semi-parametric hazards regression model: estimation of parameters, inclusion of strata, time-dependent covariates, residuals and model checking, methods for grouped or discrete lifetimes, related topics on the Cox model, rank tests for comparing distributions, estimation for semi-parametric accelerated failure time models
  • Multiple Models of Failure: Basic characteristics of model specification, likelihood functions formulation, nonparametric methods, parametric methods, semi-parametric methods for multiplicative hazards model
  • Analysis of Correlated Lifetime Data: regression models for correlated lifetime data, representation and estimation of bivariate survivor function.

Demography

  1. Shryock, H.S. and Siegel, J.S. and Larmon, A.E. (1975). The Methods and Materials of Demography. Vol-1 & 2. U.S. Department of Commerce Publication
  1. Lawless, J.F. (2003). Statistical Models and Methods for Lifetime Data. 2nd Edition. Wiley.

References

  1. Siegel, S.J. and Swanson, D.A. (2004). The Methods and Materials of Demography. 2nd Edition. Elsevier
  2. Spiegelman (1968). Introduction to Demography. Revised Edition. Harvard University Press, Cambridge
  3. Kpdekpo, G.M.K. (1982). Essentials of Demographic Analysis for Africa. Heinemann International Literature & Textbooks
  4. Kalbfleisch, J.D. and Ross, L.P. (2002). The Statistical Analysis of Failure Time Data. 2nd Edition. Wiley.
  5. Anderson J.A., Dow J.B., Actuarial Statistics VOL II Construction of Mortality and Other Tables. Cambridge University Press. Published for the Institute and Faculty of Actuaries
  6. Klein J.P., Moeschberger M.L. (2003) Survival Analysis: Techniques for Censored and truncated data. 2nd edition. Springer Verlag.
Credits 3
Pre-requisite

ASTA 508
Description

  • Introduction to Life insurance: life insurance and annuity contracts, pension benefits, mutual and proprietary insurers
  • Probability concepts: joint, marginal, and conditional probability
  • Survival Models: Actuarial notation, future lifetime random variable, force of mortality, curtate future lifetime random variable.
  • Life tables and Selection: Life tables, different life table functions and inter-relationships among them, cause specific competing risk life tables, multiple decrement life table, fractional age assumptions, national life tables, Actuarial life table, survival models for life insurance policy holders, mortality trends
  • Insurance Benefits: assumptions, valuation of insurance benefits
  • Annuities: Annual annuities, annuities payable continuously, increasing annuities, evaluating annuity functions
  • Premiums: Preliminaries, assumptions, future loss random variable, the equivalence principle
  • Policy Values: Policy with annual cash flows, policy with continuous cash flows, policy alterations
  • Multiple State Models: Alive Dead Model, Permanent disability model, the disability income insurance model, Markov multiple state models in discrete time,
  • Joint Life and Last Survivor Benefits:  Joint life and last survivor benefits, a multiple state model for independent future lifetimes, a model with dependent future lifetimes, the common shock model.
  • Pension Mathematics: Summary, Salary Scale Function, Valuation of Benefits, Service table
  • Yield curves and Non-diversifiable Risk: Yield Curve, valuation of Insurances and Life annuities, Diversifiable and non-diversifiable Risk, Monte Carlo Simulation
  • Emerging Costs for Traditional Life Insurance: Introduction, profit testing a term insurance policy, Profit testing Principles, Profit measures, Profit testing Multiple State Models
  • Simulation: The Inverse Transform method, The Box Muller method, The Polar method

Text Book:

  1. Dickson, D.C.M., Hardy, M.R. and Waters, H.R. (2013). Actuarial mathematics for life contingent risks. 2nd Edition. Cambridge University Press

References

  1. Benjamin, B. and Pollard, J.H. (1993). The Analysis of Mortality and other Actuarial Statistics. 3rd Edition. Institute and Faculty of Actuaries
  2. Jordan, C.W. (1975). Life Contingencies. 2nd Edition. Chicago: Society of Actuaries
  3. Moller T., and Steffensen M. (2007) Market Valuation Method in Life and Pension Insurance. Cambridge University Press
  4. Hooker P.F. and Logley-Cook L.H. Life and Other Contingencies VOL I. Cambridge University Press. Published for the Institute and Faculty of Actuaries.
  5. Newton L. Bpwers, hans, U.gerber, Jame, C. Hickman, Donald, A. Jones, Cecil, J. Nesbitt (1997). Actuarial Mathematics. 2nd edition. Society of Actuaries.
  6. Sohrab Uddin M. (1992) An Intruduction to Actuarial and Financial Mathematics
Credits 3
Pre-requisite

ASTA 509
Description

  • Risk environment: Risk management process, the design of products, schemes, contracts and other arrangements, risk classification, systematic and diversifiable risk, risk appetite and risk efficiency, credit risk and credit ratings, liquidity risk, market risk, operational risk, business risk, attitudes to and methods of risk acceptance, rejection, transfer and management for stakeholders
  • Regulatory environment: the regulatory regimes, the concept of information asymmetry, fairness of financial contracts, implications of a requirement to treat the customer fairly
  • External environment: implications of: legislation – regulations, State benefits, tax, accounting standards, capital adequacy and solvency, corporate governance, risk management requirements, competitive advantage, demographic changes, environmental issues, international practice
  • Investment environment: the cash-flows of simple financial arrangements and the need to invest appropriately to provide for financial benefits on contingent events, the principal economic influences on investment markets, relationships between the total returns and the components of total returns, on equities, bonds and cash, and price and earnings inflation.
  • Capital requirements: the main providers of benefits on contingent events need capital, the implications of the regulatory environment, measures of capital needs, economic balance sheet, in order to consider the capital requirements of a provider of benefits on contingent events
  • Contract design: the factors to be considered in determining a suitable design for financial structures e.g. products, schemes, contracts or other arrangements
  • Project planning and management: the process of project management, actuarial techniques of capital investment projects and cost-benefit analyses
  • Data: the data requirements for determining values for assets, future benefits and future funding requirements, the ideal data, the appropriate grouping of data
  • Risk management: the issues surrounding the management of risk, tools and methods of measuring risk, risks with low likelihood but high impact, the use of scenario analysis, stress testing and stochastic modelling in the evaluation of risk
  • Modelling: the use of actuarial models, requirements for building a model, project future cash and revenue flows, the use of these models for– pricing or setting future financing strategies – risk management – assessing the capital requirements – pricing and valuing options and guarantees, sensitivity analysis of the results of the models; Assumption setting; Expenses; Developing the cost and the price; Investment management; Provisioning; Relationship between assets and liabilities
  • The solution: Maintaining profitability, Determining the expected results; Reporting actual results; Asset management; Capital management; Surplus management; Insolvency and closure; options and guarantees;
  • Monitoring: the actual experience can be monitored and assessed in terms of: monitoring experience, the data required, the various factors affecting the experience, revised models and assumptions.

Text Book

  1. Allen, S.L., Financial Risk Management: A Practitioner’s Guide to Managing Market and Credit Risk, 2nd Edition, Wiley.

References:

  1. Denuit,M.; Dhaene,J.; Goovaerts,M.; Kaas,R.,(2005), Actuarial Theory for Dependent Risks: Measures, Orders and Models, Wiley
  2. Brown,A., Financial Risk Management For Dummies, 3rd edition, Wiley.
  3. Hardy,M.,(2003), Investment Guarantees: Modeling and Risk Management for Equity-Linked Life, Wiley
  4. Poitras,G., Risk Management, Speculation, and Derivative Securities, 1st Academic Press.
  5. Sweeting,P., Financial Enterprise Risk Management,  1st edition, Cambridge University Press.
Credits 3
Pre-requisite

ASTA 510
Description

Statistical analysis using R, SPSS or SAS for the following topics-

Linear regression analysis: parameter estimates, ANOVA, and tests of significance

Non-linear regression analysis: parameter estimates, confidence intervals and hypothesis tests; One factor and two factor factorial experiments and tests; Large data management

Multivariate analysis: Principal component analysis; Factor analysis; Cluster analysis; Profile analysis; other multivariate analysis

Generalized Linear Model, general logistic regression, maximum likelihood estimation and log-likelihood ratio statistic and Generalized Estimating Equation, Cox PH model

Text Book: Everitt, B. and Hothorn, T. (2006). A Handbook of Statistical Analyses Using R.
Chapman & Hall/CRC, Boca Raton, FL. ISBN 1-584-88539-4

Reference

  1. Dalgaard, P. (2008). Introductory Statistics with R. Springer, 2nd Edition, ISBN 978-0387-79053-4
  2. Der, G. and Everitt, B.S. A Handbook of Statistical Analysis Using SAS. 3rd Edition. CRC Press
Credits 3
Pre-requisite

ASTA 511
Description

  • Modern probability: probability as a set function; Borel field and extension of probability measure; probability measure notion of random variables; probability space; distribution function; expectations and moments, convergence of random variables, Laplace transformation
  • Stochastic Process: Introduction, distinction between deterministic and stochastic models, Random Walk, concept and properties of discrete random walks and random walks with normally distributed increments, both with and without drift
  • Markov Chain: introduction, transition probability matrices of a Markov chain, first step analysis, some special Markov chains, regular transition probability matrices, classification of states; basic limit theorem of Markov chain; reducible Markov chains;
  • Poisson process: counting and Poisson process; the law of rare events
  • Continuous time Markov chain: pure birth processes; pure death processes; birth and death processes; limiting behavior of birth and death processes; birth and death process with absorbing states; finite state continuous time Markov chains
  • Renewal theory and its applications: introduction, distribution of N(t), limit theorems and their applications, renewal reward process regenerative process, semi-Markov process
  • Queuing Process
    • the connection between Poisson process and the Poisson distribution, Poisson process as
    • the distribution of waiting between events
    • the distribution of process increments
    • the behavior of the process over an infinitesimal time interval
  • Compound Processes: Compound Binomial, Compound Poisson, Compound Negative Binomial Random variables

Text Book

  1. Taylor, H.M. and Karlin, S. (1998). An Introduction to Stochastic Modeling. 3rd Edition. Academic Press

References:

  1. Ross, S. (2003). Introduction to Probability Models. 8th Edition. Elsevier
  2. Grimmett, G. and Stirzaker, D. (2001). Probability and Random Processes. 3rd Edition. Oxford University Press, USA.
  3. Karlin S. and Taylor H.M. (1975). A First Course in Stochastic Processes. 2nd Edition.  Academic Press. ISBN 0-12-398552-8
  4. Bailey, N.T.J. (1964). The Elements of Stochastic Processes with Applications to the Natural Sciences. John Wiley
  5. Bartlett, M.S. (1978). An Introduction to Stochastic Processes. 3rd Edition. Cambridge University Press. Wiley, NY
  6. Grandell J. (1997). Mixed Poisson Process. Chapman and Hall
  7. Kijima M. (2000). Stochastic Processes with applications to Finance. Chapman and Hall

 

 

Credits 3
Pre-requisite

ASTA 512
Description

  • Basic concepts and introduction: utility function and utility theory, the economic properties of commonly used utility functions, dependent utility functions, utility maximization, economic characteristics of consumers and investors: non-satiation risk aversion, risk neutrality and risk seeking ,declining or increasing absolute and relative risk aversion, the traditional theory of consumer choice, utility functions to compare investment opportunities, for first and second-order dominance, behavioral finance.
  • Investment risk: measures of investment risk: variance of return, downside semi-variance of return, shortfall probabilities, Value at Risk (VaR) / Tail VaR, investor’s utility function, investment opportunities, distribution of returns, thickness of tails, assessment of risk.
  • Mean-variance portfolio theory: assumptions of mean-variance portfolio theory, application of mean-variance portfolio, optimum portfolio, diversification using mean-variance portfolio theory.
  • Single and multifactor models: multifactor models: macroeconomic models, fundamental factor models, statistical factor models, single index model, diversifiable and non-diversifiable risk, construction of multifactor models.
  • The principal results, assumptions and limitations: Sharpe-Lintner-Mossin Capital Asset Pricing Model (CAPM), the theory to overcome these limitations, the Ross Arbitrage Pricing Theory model (APT)
  • Efficient Markets hypothesis: Efficient Markets Hypothesis for investment management, the evidence for or against each form of the Efficient Markets Hypothesis.
  • Stochastic models of the behavior of security prices: security prices and the empirical evidence, auto-regressive models, Wilkie model, data availability, data errors, outliers, stationarity of underlying time series, the role of economic judgment.
  • Brownian motion (or Wiener Processes): standard Brownian motion, stochastic differential equations, the Ito integral, diffusion, mean-reverting processes, Ito’s formula, the stochastic differential equation for geometric Brownian motion, equation for the Ornstein-Uhlenbeck process.
  • Option prices, valuation, hedging: arbitrage and a complete market, option prices, forward contract, call and put options, put-call parity, binomial trees and lattices in valuing options, binomial lattice, the pricing of equity options, the real-world measure, the risk-neutral measure, the risk-neutral, state-price deflator approaches, the Black-Scholes derivative-pricing model: a complete market, risk-neutral pricing, the equivalent martingale measure, the Black-Scholes partial differential equation, price and hedge, the Black-Scholes model, binomial model, the Black-Scholes model, the risk-neutral pricing approach, the commonly used terminology, partial derivatives (the Greeks) of an option price.
  • Interest rates: the term-structure of interest rates, the pricing of zero coupon bonds, interest-rate derivatives, one-factor diffusion model, the risk-free rate of interest, state-price deflators, zero-coupon bonds and interest-rate derivatives, the Vasicek, Cox-Ingersoll-Ross and Hull-White models, one-factor models, simple models for credit risk, the terms credit event, recovery rate, structural models, reduced form models, intensity-based models, the Merton model, two-state model, constant transition intensity, the Jarrow-Lando-Turnbull model, the two-state model, stochastic transition intensity.

Text Book

  1. Panjer, H. H 2001, Financial economics: with applications to investments, insurance and pensions. The Actuarial Foundation.

Reference

  1. Baxter M., Rennie A. 1996. Financial calculus: an introduction to derivative pricing. CUP.
  2. Cairns, Andrew J. G. 2004 Interest rate models: an introduction. Princeton University Press.
  3. Joshi, MS. Paterson, JM. 2013 Introduction to mathematical portfolio theory. Cambridge University Press.
  4. Elton EJ, Gruber, MJ, Brown, SJ. et al. 2014 Modern portfolio theory and investment analysis. 9th ed. John Wiley.
  5. Karatzas I., Sharve S.E. (1998) Methods of Mathematical Finance. Spring Verlag
  6. Musiela M., Rutkowska M. (2007). Martingale Methods in Financial Modeling. 2nd Edition. Spring Verlag

 

Credits 3
Pre-requisite

ASTA 513
Description

  • Basic econometric models, assumptions, and parameter estimation
  • Multicollinearity: nature, detection, consequence and remedy of multicollinearity
  • Autocorrelation: definition, detection, consequence and remedy
  • Heteroscedasticity: definition, detection, consequence and remedy
  • Model Specification: Consequences of under and over specification, model selection criteria
  • Estimation and application of Cobb-Douglas production function
  • Simultaneous equation models:
    • Simultanious equation bias
    • Inconsistance of OLS estimations
    • Types and rules of identification
    • Estimation of simultanious estimation methods: Methods of indirect least- square (ILS) and two stage least square (2 SLS)
  • Non-Linear regression:  
    • Least Square Estimation,
    • Estimating the Parameter: Response surface methodology, Semilogarithm
    • Time series Econometrics: Stationarity, Unit roots and co-integration, Spurious regression, Dynamic Econometrics model, Distributed lag models.
  • Panel Data Models: 
    • Fixed Effects
    • Random Effects
    • Dynamic Model
  • Introduction to Time Series: examples of time series, objectives, types of variation, stationarity, trends and seasonal components, no seasonal component, time plot
  • Autocovariance of a Stationary Time Series: Stationarity, applied to stationary time series, drawbacks of shift operator, backwards difference, the spectral density, time series models, Box-Jenkins model, concept of a filter, root characteristic equation of time series, estimation of the mean and the autocovariance, Multivariate Autoregressive model;

AR process, MA process, ARMA processes, calculation of the ACVF, Prediction of an ARMA Process, cointegrated time series, ARIMA time series

  • Forecasting: Introduction, univariate procedures, multivariate procedures, comparative review of forecasting procedures, prediction theory

Text Book

  1. Gujarati, Damodar N. Basic Econometrics. New York: McGraw-Hill, Fifth Edition.
  2. H. Greene (2011). Econometric Analysis. 7th Edition. Prentice Hall.

References:

  1. M. Wooldridge (2010). Econometric Analysis of Cross Section and Panel Data. 2nd Edition. The MIP Press.
  2. M Verbeek (2000). A guide to Modern Econometrics. 3rd Edition, John Wiley & Sons
  3. Makridakis S., Wheelwright C., and Hyndman R. J. (1997) Forecasting Methods and Applications, 3rd Edition, Wiley.
  4. Chatfield, C. (2003). The Analysis of Time Series. 6th Edition, Chapman Hall.

 

Credits 3
Pre-requisite

ASTA 514
Description

  • Legislative and regulatory framework for investment: knowledge of the legislative and regulatory framework for investment management and the securities industry in Bangladesh
  • The framework of regulation of investment industry: the relevant professional guidance for actuaries working in the investment field, The Insurance Act 2010, Insurance Act 1938, Insurance Development and Regulatory Authority Act 2010, Insurance Corporation Act 1973, Rules and Regulations made under the Insurance Act 2010, the circumstances in which actuaries require authorization under the Financial Services and Markets Acts,
  • The taxation treatment: The taxation treatment of different forms of investment for individual and institutional investors
  • The principles and objectives of investment management and analyses: Analyses the particular liability characteristics, investment requirements and the influence of the regulatory environment on the investment policies, life insurance company policies, general insurance company, health and care insurance company, self-administered defined benefit pension fund, self-administered defined contribution pension fund, pure fund manager,  the investment vehicles into account taxation, expenses and other relevant considerations
  • The investment indices and global investors
  • The principal techniques in portfolio management including risk control techniques; the principal active management “styles” (value, growth, momentum, rotational), passive fund management, investment management assessment and selection, investment management of a large portfolio, structure of an institutional investment department, performance measurement service
  • The principal investment assets and the markets: the processes of dealing, transfer and settlement processes in the main equity, bond and derivative markets, the processes of dealing, transfer and settlement processes in the main overseas equity, bond and derivative markets, levels of charges, expenses and dealing spreads for an institutional investor, main features of the capital markets in the developed and emerging markets.
  • Specialist investment assets and the markets: asset-backed securities, unquoted equities, including venture capital (“private equity”) investment, property finance and development, Analyses more complex problems in terms of actuarial, economic and financial factors to a level where appropriate analytical techniques, and interpret the results in a wider context and draw appropriate conclusions.

 Text Book

  1. Bodie, Z., Kane, A., Marcus, A. J. (2011). 9th ed. McGraw-Hill.

References:

  1. Chandra, P. Investment Analysis and Portfolio Management. Fourth Edition. Tata McGraw Hill.
  2. Tavakoli, J.M. (2001). Credit derivatives and synthetic structures: a guide to instruments and applications. 2nd Wiley.
  3. Clark, G. (2007). A Farewell to Alms: a brief economic history of the world. Princeton University Press.
  4. Saunders, A. (2011), Foreign exchange risk [in: Financial institutions management: a modern perspective]. 7th ed. McGraw-Hill.
  5. Hull, J. C. Options, futures and other derivatives. 8th ed. Pearson.

 

Credits 3
Pre-requisite

AST-101
Description

Statistics and its origin:
Defining Statistics, Characteristics of Statistics, Uses & Importance of Statistics, Population & Sample; sources of Statistical Data, Parameter and Statistic.

Summarizing Data:
Meaning of Data, Level of Measurement, Variable and attribute, Summarizing and Presenting Data, Frequency Distribution, Formation of Discrete and Continuous Frequency Distribution, Cumulative Frequency Distribution, Presenting Data by Graphs and Diagrams, Presentation of Qualitative Data, Presentation of Quantitative Data.

Descriptive Statistics I: Measures of Central Tendency
Measures of central tendency, arithmetic mean, median, quartiles, percentiles and deciles, mode, geometric mean, harmonic mean, other measures of average, comparing the averages, properties of measures, effects of change in origin and scale, stem and leaf plot

Descriptive Statistics II: Measures of Dispersion
Meaning of dispersion, measures of dispersion, absolute measures of dispersion, relative measures of dispersion, empirical relations among measures of dispersion, comparing the measures, moments, central moments in terms of raw moments, effects of change in origin and scale on moments, Sheppard’s correction for moments, shape characteristics of a distribution, box and whisker plots.

Simple Linear Regression and Correlation:
Correlation analysis, measuring the correlation, rank correlation, regression analysis, simple linear regression model, scatter diagram, leAST- square method, properties of regression coefficient, partitioning of the total variation in regression, Coefficient of multiple determination

References:

  1. Mostafa, M.G. (1989). Methods of Statistics. Dhaka : Karim Press & Publication
  2. Daniel, W. (2009). Biostatistics: Basic Concepts and Methodology for the Health Science. 9th Edition. WSE
  3. Hoel, P. G. (1984). Introduction to Mathematical Statistics.5th Edition. John Wiley, NY
  4. Wonnacott, T.H. & Wonnacott, R.J. (1990). Introductory Statistics. 5th Edition. John Wiley, NY
  5. Yule, G.U. and Kendall, M.G. (1968). An Introduction to the Theory of Statistics. 14th Edition. Charles-Griffin, London
  6. Islam, M.N. (2004). An Introduction to Statistics and Probability. 3rd Edition. Mullick Brothers.

 

Credits 3
Pre-requisite

AST-102
Description

  • Meaning of probability; definition and scope of probability;
  • Set theory; sample space; elements of set theory; axiomatic definition of probability;
  • permutation and combinations;
  • conditional probability and rules of probability for dependent and independence cases;
  • Bayes theorem;
  • Random variables; probability function and probability density function;
  • Distribution function; joint probability function; marginal and conditional distributions.
  • Mathematical expectations; expectations of sums and products of random variables; variance
  • Conditional expectation and variance; Cauchy-Schwartz, Markov and Chebysheb inequality
  • Evaluation of probabilities (by calculation or by referring to tables as appropriate with the distributions.
  • Moment and cumulant generating functions; characteristic function; probability generating function; (definitions and only for discrete distributions)

References:

  1. Ross, S. (2012). A First course in Probability. 9th Pearson Prentice Hall, NJ
  2. Rohatgi, V.K. and Saleh, A.K.M. (2000). An Introduction to Probability and Statistics. 2nd A Wiley-Interscience Publication
  3. Meyer P.L. (1970). Introductory Probability and Statistical Applications. Addison-Wesley, USA
  4. Mosteller F., Rourke E.K.R. and Thomas G.B. (1970). Probability with Statistical Applications. 2nd Edition. Addison-Wesley, USA

 

Credits 3
Pre-requisite

AST-201
Description

  • Random variables; probability mass function, cumulative density function and probability density function
  • Discrete Probability Distributions: Bernoulli, binomial, Poisson, geometric, negative binomial, Hypergeometric, uniform
  • Continuous Probability Distributions: uniform, exponential, gamma, beta, normal, log- normal, Weibull
  • Identification of Moment and cumulant generating functions; characteristic function of discrete and continuous distributions
  • Showing moments from Moment and cumulant generating functions; characteristic function
  • Distribution of a function of a random variable from the distribution of a random variable
  • Determination of probability generating function of discrete and integer-valued random variables
  • Application of PGF, MGF, CGF and cumulants and the reason of their use
  • Joint, Marginal and conditional distributions
  • Law of large numbers; and central limit theorem.
  • Cauchy-Schwartz, Markov and Chebysheb inequality

References:

  1. Ross, S. (2012). A first course in Probability. 9th Edition. Pearson Prentice Hall, NJ
  2. Mood, A.M., Graybill, F.A. and Boes. D.C. (1974). Introduction to the theory of Statistics. 3rd McGraw-Hill
  3. Rohatgi, V.K. and Saleh, A.K.M. (2000). An Introduction to Probability and Statistics. 2nd Edition. A Wiley-Interscience Publication

 

Credits 3
Pre-requisite

AST-202
Description

  • Sampling and Sampling Distributions.
  • Expectations of functions of random variables: expectation two ways, sums of random variables, product and quotient;
  • Independence of random variables, mean and variance of linear combinations of random variables
  • Deriving distributions of the linear combinations of random variables
  • Cumulative distribution function technique: distribution of minimum and maximum, distribution of sum of difference of two random variables, distribution of product and quotient;
  • Moment generating function technique: description of technique, distribution of sums of independent random variables; The transformation Y = g(X): distribution of Y = g(X), probability integral transformation;
  • Transformations: discrete random variables, continuous random variables;
  • Sampling: basic concepts of random samples, inductive inference, populations and samples, distribution of samples, statistic and sample moments; Sample mean: mean and variance
  • Central limit theorem, normal approximations to other distributions, continuity correction
  • law of large numbers, central limit theorem, Bernoulli and Poisson distribution, exponential distribution, uniform distribution, Cauchy distribution;
  • Sampling from the normal distributions: role of normal distribution in statistics, samples mean, chi-square distribution, the F-distribution, Student’s t-distribution.
  • Non-central distributions: non-central chi-squared, t, and F distributions; definitions, derivations, properties

References:

  1. Ross, S. (2012). A first course in Probability.9th Edition. Pearson Prentice Hall, NJ
  2. Mood, A.M., Graybill, F.A. and Boes. D.C. (1974). Introduction to the theory of Statistics. 3rd McGraw-Hill
  3. Hogg, R.V. and Craig, A.T. (2012). Introduction to Mathematical Statistics. 7th Pearson
  4. Rohatgi, V.K. and Saleh, A.K.M. (2000). An Introduction to Probability and Statistics. 2nd A Wiley-Interscience Publication

 

Credits 3
Pre-requisite

MAT 101
Description

Differential Calculus: Functions; Basic concept of limits and continuity; Slopes and Rates of change; Techniques of differentiation, Successive differentiation, Leibnitz theorem, Indeterminate forms, Analysis of Function: Function increasing, Function decreasing, Concavity of a curve, Points of inflection, Rolle’s Theorem, Mean-Value Theorem, Taylor’s Theorem; Applications of Derivative; Maxima and minima of a function; Functions of two or more variables; Partial Derivatives, Euler’s theorem on homogeneous function.

Integral Calculus: Integration by the method of substitution, by parts. Integration of rational functions by partial fractions, Definite integrals and its properties and use in summing series. Beta function and Gamma function. Applications of definite integrals: Area under a plane curve and area of a region enclosed by two or more curves in Cartesian co-ordinate system, volumes of solids generated by revolution, volumes of hollow solids of revolution by shell method, multiple integrals with application; Jacobeans.

Text Book: Calculus: Howard Anton, Irl Bivens & Stephen Davis, 10th edition, John Wiley & Sons.

Reference      

  1. Differential Calculus: Das & Mukherjee.
  2. Integral Calculus: Das & Mukherjee.

 

Credits 3
Pre-requisite

MAT206
Description

  • Theory of Numbers: Unique factorization theorem, congruencies, Euler’s phi-function
  • Inequalities: Order properties of real numbers, Weierstrass’, Chebysev’s and Cauchy’s inequalities, inequalities involving means.
  • Complex Numbers: Field properties, geometric representation of complex numbers, operations of complex numbers.
  • Summation Series: Summation of algebraic and trigonometric finite series.
  • Theory of equations: Relation between roots and coefficients, symmetric functions of roots, Descartes rule of signs, rational roots, Newton’s method.
  • Linear Algebra: Systems of linear equations and matrices: Introduction to systems of linear equations, Gaussian elimination, Matrices and matrix operations, Inverses; rules of matrix arithmetic, Elementary matrices and a method for finding inverse of a matrix, Further results on systems of equations and invertibility, Diagonal, triangular, and symmetric matrices.
  • Determinants: Basic concept on determent, Evaluating determinants by row reduction, Properties of the determinant function, Cofactor expansion; Cramer’s rule.
  • General vector space: Real vector space, Subspace, Linear independence, Basis and dimension, Row space, column space and null space, Rank and nullity.
  • Inner product spaces: Inner products, Angle and orthogonality in inner product spaces, Orthonormal bases; Gram-Schmidt process; QR-decomposition, Best approximation; least squares, Orthogonal matrices.
  • Eigenvalues and eigenvectors: Concepts on eigenvalues and eigenvectors,
  • Linear transformation: General linear transformation, Kernel and range, Inverse linear transformations, Matrices of general linear transformations.

Text Book: (a) Higher Algebra, Md. Abdur Rahman

(b) Elementary Linear Algebra (ninth edition) – Howard Anton and Chris Rorres

(c) Theory and Problems of Complex Variables – Murray R. Spiegel

 

Reference

(a) Number Theory – S G Telang

(b) Complex Variables and Its Applications – R. V. Churchill

(c) Experiments in Computational Matrix Algebra    – David R. Hill

(d) Higher Engineering Mathematics – Grewel (36th edition)

 

Credits 3
Pre-requisite
+ Master of Science in Applied Statistics

AST- 501
Description

  • Design and implementation of Surveys with the following sampling design:
  • Simple Random Sampling, Systematic Sampling, Stratified Sampling, Cluster Sampling,
  • Questionnaire design and formatting
  • Multistage and Multiphase Sampling
  • Estimation of sample size for different sampling design in order to estimate population level point estimates and testing null hypothesis
  • Application of intra-class correlation of design effects for complete survey
  • Estimation of design weight and adjustment for non response
  • Examples of various national and international Surveys
  • Detailed discussion on Bangladesh Demographic Health Surveys (Important)

Reference: 

  1. United Nations Department of Economic and Social Affairs: Designing Household Survey Samples, United Nations, 2005
  2. Lohr S. L. (2009). Sampling Design and Analysis. Duxbury Press
  3. Levy P.S. and Lemeshow, S. (1999). Sampling of Populations: Methods and Applications, 3rd Edition, New York: Wiley Interscience
  4. Cochran, W.G. (1977).Sampling Techniques.3rd John Wiley and Sons Inc.
  5. Des Raj (1968).Sampling Theory. McGraw-Hill Inc.
Credits 3
Pre-requisite

AST – 502
Description

  1. Simple Regression Models: Review
  2. Multiple Regression Models and Estimation
  • Matrix Notation and Literacy
  • Hyper plane extension to simple linear model
  • Interaction models
  • Basic estimation and inference for multiple regression
  • Related Application

3. General Linear F test and Sequential SS

  • Reduced and Full models
  • F test for general linear hypotheses
  • Effects of a variable controlled for other predictors
  • Sequential SS
  • Partial correlation
  • Related Application

4. Multicollinearity among independent variables

  • Effect on standard deviations of coefficients
  • Problems interpreting effects of individual variables
  • Apparent conflicts between overall F test and individual variable t test
  • Benefits of designed experiments
  • Related Application
  1. Polynomial Regression Models

     6. Categorical Predictor Variables 

  • Dummy Variable Regression
  • Interpretation of models containing indicator/Dummy variables
  • Piecewise regression
  • Related Application

    7. More Diagnostic Measures and Remedial Measures for Lack of Fit

  • Variance Inflation Factors
  • Ridge Regression
  • Deleted Residuals
  • Influence statistics – Hat matrix, Cook’s D and related measures
  • Related Application

    8. Examining All Possible Regressions

  • R2, MSE , Cp
  • Stepwise algorithms
  • Related Application

    9. Nonlinear Regression      

  • Logistic and Poisson regression models
  • Probit Model, Tobit Model
  • Related Application

Reference

  1. Draper, N.R. and Smith, H. (1999). Applied Regression Analysis. 3rd Wiley
  2. Kutner, Nachtsheim, and Neter (2004). Applied Linear Regression Models. 4th Edition, McGraw Hill
  3. Weisberg,S. (2005). Applied Linear Regression. 3rd Edition, Wiley
  4. Gujarati, Damodar N, Basic econometrics.  4th ed. Publisher: Neu delhi ; Tata McGraw-Hill, c2003
Credits 4
Pre-requisite

AST- 503
Description

  • A theoretical treatment of statistical inference (sufficient statistics, minimal sufficient statistics, ancillary statistics, complete statistics)
  • Point estimation methods and properties
  • Interval estimation
  • Hypothesis testing
  • Asymptotic evaluation
  • Estimation and hypothesis testing in regression
  • Analysis of variance
  • Chi-square tests
  • Non-Parametric Tests
  • Bayesian techniques

Text book              

Hogg, R.V. McKean, J. and Craig, A.T. (2012). Introduction to Mathematical Statistics. 7th Edition. Pearson Education, Limited

References

  1. Mood, A.M., Graybill, F.A. and Boes. D.C. (1974). Introduction to the Theory of Statistics. 3rd McGraw-Hill.
  2. Casella G, and Berger RL (2002), Statistical Inference, 2nd Brooks/Cole.
  3. Kvam, P.H. and Vidakovic B. (2007). Nonparametric Statistics with Applications to Science and Engineering.
  4. Sprent, P. and Smeeton, C. (2001). Applied Nonparametric Statistical Methods.3rd Edition. Chapman & Hall/CRC.
  5. Kendall, M., Stuart, A. and Ord, J.K. (1998). Kendall’s Advanced Theory of Statistics, Distribution Theory. Vol 1. 6th Edition. Oxford University Press, USA
  6. Kendall, M., Stuart, A. and Ord, J.K. (1999). Kendall’s Advanced Theory of Statistics, Classical Inference and the Linear Model. Vol 2. 6th Edition. Oxford University Press, USA
Credits 3
Pre-requisite

AST- 504
Description

Introduction, Preview of Linear Models and Analysis of Variance Models, One Way of Classification, Partition of Sum of Squares, Mean Squares and Expectations, Fixed and Random Effect Models, Tests, Intra-class Correlation and Variance Ratio Confidence Intervals, Analysis of Variance for Unbalanced Data, Estimates, Confidence Intervals, Inference about Difference between Treatment Means, Multiple Comparisons, Effects and Tests of Departures from Assumptions Underlying the Analysis of Variance Model,  Two Way Crossed Classification without Interaction, Model, Assumptions, Mean Squares and Expected Mean Squares, Fixed Effects, Random Effects, Mixed Effects, Tests, Two Way Crossed Classification with Interaction. Model, Assumption, Partition of SS, Mean Squares and Expectations, Fixed Effect, Random Effect and Mixed Effects, Tests, Models for Unbalanced Data.

Two Way Nested (Hierarchical) Classification, Model, Assumptions, Fixed Effects, Random Effects and Mixed Effects, Estimation and Tests, Multivariate Analysis of Variance, Repeated Measures Data and ANOVA, Multilevel Models

References

  1. Rencher, A.C. (2000). Linear Models in Statistics. John Wiley and Sons, New York
  2. Sahai, H. and Ageel, M.I. (2000). The Analysis of Variance. Birkhauser, Boston
  3. Christensen, R. (1998). Analysis of Variance, Design and Regression. Chapman and Hall, London
  4. Sahai, H. and Ojeda, M.M. (2004). Analysis of Variance for Random Models. Birkhauser, Boston
  5. Montagomery D. C. (2001): Design & Analysis of Experiments. 5th Edition. Wiley
Credits 4
Pre-requisite

AST- 505
Description

Statistical analysis using R or SAS for the following topics-

  • Multivariate analysis
  • Principal component analysis
  • Factor analysis
  • Cluster analysis
  • Profile analysis
  • Other multivariate analysis
  • Generalized Estimating Equation
  • Generalized Linear Model
  • Advance linear regression analysis
  • Non-linear regression analysis
  • Model fitting and tests.
  • Large data management

Reference:

  1. Johnson, R.A. and Wichern, D.W. (2007). Applied Multivariate Statistical Analysis. 6th Prentice-Hall
  2. Dalgaard, P. (2008). Introductory Statistics with R. Springer, 2nd Edition, ISBN 978-0387-79053-4
  3. Everitt, B. and Hothorn, T. (2006). A Handbook of Statistical Analyses Using R. Chapman & Hall/CRC, Boca Raton, FL. ISBN 1-584-88539-4
  4. Der, G. and Everitt, B.S. A Handbook of Statistical Analysis Using SAS. 3rdCRC Press
Credits 4
Pre-requisite

AST- 506
Description

  • Comparisons of several multivariate means: paired comparisons and a repeated measures design; comparing mean vectors from two populations;
  • comparison of several multivariate population means (one-way MANOVA); simultaneous confidence intervals for treatment effects; two-way multivariate analysis of variance;
  • profiles analysis; repeated measures designs and growth curves;
  • Multivariate linear regression models: the classical linear regression model; least squares estimation;
  • inferences about regression model; inferences from the estimated regression function; model checking;
  • Multivariate multiple regression; comparing two formulations of the regression model; principal components
  • factor analysis
  • canonical correlation analysis
  • Discrimination and classification
  • Cluster analysis

Text Book

1.  Johnson, R.A. and Wichern, D.W. (2007). Applied Multivariate Statistical Analysis. 6th Edition. Prentice-Hall

Credits 4
Pre-requisite

AST- 507
Description

  • Introduction to the Concepts of Modeling,
  • Model Fitting: Examples, Some Principles of Statistical Modeling (Exploratory Data Analysis, Model Formulation, Parameter Estimation, Residuals and Model Checking), Estimation and Tests Based on Specific Problems
  • Sampling Distribution for Score Statistics, MLEs, Deviance; Log-likelihood ratiom Statistic,
  • Exponential Family and Generalized Linear Models (Bernoulli, Binomial, Poisson, Exponential, Gamma, Normal, etc.),
  • Properties of distributions in the exponential family, expected value, variance, expected value and variance of score statistic, examples for various distributions.
  • Components of Generalized Linear Models- Random, Systematic and Link Functions, Poisson Regression.
  • Maximum Likelihood Estimation Using Chain Rules.
  • Random Component, Mean and Variance of the Outcome Variable, Variance Function, Dispersion Parameter, Applications.
  • Systematic Component and Link Function: Identity Link, Logit Link, Log Link, Parameter Estimation.
  • Score Function and Information Matrix, Estimation Using the Method of Scoring, Iteratively Reweighted Least Squares.
  • Inference Procedures, Deviance for logit, identity, log link functions, Scaled Deviance, Sampling Distributions, Hypothesis Testing.
  • Generalized Pearson Chi square Statistic, Residuals for GLM, Pearson Residual, Anscombe Residuals.
  • Logit Link Function, Iteratively Reweighted Least- Squares, Tests;
  • Nominal and Ordinal Logistic Regression.
  • Goodness of Fit Tests, Hosmer-Lemeshow Test, Pseudo R square, AIC and BIC.
  • Quasi Likelihood, Construction of quasi likelihood for correlated outcomes, Parameter Estimation, Variance-Covariance of Estimators, Estimation of Variance function.
  • Quasi Likelihood Estimating Equations, Generalized Estimating Equations for Repeated Measures Data, Repeated Measures Models for Normal data, Repeated Measures Models for Non-Normal Data, Working Correlation Matrix, Robust Variance Estimation or Information Sandwich Estimator, Hypothesis Testing.
  • Comparison between Likelihood and Quasi Likelihood Methods, Mixed Effect Models.

References

  1. Dobson, A.J. and Barnett, A.G. (2008). An Introduction to Generalized Linear Models. 3rd Chapman and Hall/CRC, Florida
  2. McCullagh, P. and Nelder, J.A. (1989). Generalized Linear Models. 2nd Edition, Chapman and Hall, New York.
  3. Hosmer,D.W., Lemeshow, S. and  Sturdivant, R.X. (2013). Applied Logistic Regression. 3rd Edition. Wiley, New York.

 

Credits 4
Pre-requisite

AST- 508
Description

  • Introduction: Examples, simple descriptive techniques, trend, seasonality, the correlogram. White noise (WN), Transformation to stationarity, Stationary Time series with practical examples.
  • Probability models for time series: stationarity. Moving average (MA), Autoregressive (AR), ARMA, ARIMA, SARIMA models with applications to economics, engineering and biomedical sciences.
  • Estimating the autocorrelation function and fitting ARIMA models.
  • Forecast-ing: Exponential smoothing, Forecast-ing from ARIMA models.
  • Stationary multivariate models: Stationary multivariate models with application to real life data. Dynamic simultaneous equations models, Vector autoregression (VAR) models, Granger causality, Impulse response functions, Variance decompositions, Structural VAR
  • Nonstationary Multivariate models: Nonstationary Multivariate models with examples. Spurious regression, Cointegration, Granger representation theorem, Vector error correction models (VECMs), Structural VAR models with cointegration, testing for cointegration, estimating the cointegrating rank, estimating cointegrating vectors.
  • Stationary processes in the frequency domain: The spectral density function, the periodogram, spectral analysis with Empirical aspects of spectral analysis State-space models: Dynamic linear models and the Kalman filter with applications of filter.

 References

  1. Robert H. Shumway and David S. Stoffer (2010): Time Series Analysis and Its Applications With R Examples.3rd Springer. ISBN: 9781441978646
  2. Box, G.E.P. Jankins, G.M. and Reinsel G.C. (2008): Time series Analysis (Forecasting and control). 4th edition, Wiley
  3. Cryer, J.D. and Chan K.S. (2009): Time Series Analysis with Applications in R. 2nd Edition, Springer
  4. Chatfield, C. (2003): The Analysis of Time Series: An Introduction. 6th Edition. Chapman & Hall/CRC
  5. Brockwell, P.J. and Davis, R.A. (2009). Time Series: Theory and Methods. 2nd Springer
  6. Wheelwright, S.C. and Makridakis, S. G. (1989). Forecasting Methods for Management, 5th Wiley, New York.
  7. Anderson, T.W. (1971). The Statistical Analysis of Time series. 1st Edition. John Wiley, New York

 

Credits 4
Pre-requisite

AST- 509
Description

Review of: Contingency table, Inference of contingency table, GLM for binary and count data, Inference of logistic regression.
Logit Models for Multinomial Responses
Nominal Responses: Baseline-Category Logit Models; Ordinal Responses: Cumulative Logit and link Models; Alternative Models for Ordinal Responses; Testing Conditional Independence in I×J×K Tables; Discrete-Choice Multinomial Logit Models.
Loglinear Models for Contingency Tables
Loglinear Models for Two-Way Tables; Loglinear Models for Independence and Interaction in Three-Way Tables; Inference for Loglinear Models; Loglinear Models for Higher Dimensions; The Loglinear_Logit Model Connection.
Building and Extending Loglinear / Logit Models
Modeling Ordinal Associations; Association Models; Association Models, Correlation Models, and Correspondence Analysis; Poisson Regression for Rates; Empty Cells and Sparseness in Modeling Contingency Tables.
Models for Matched Pairs
-Comparing Dependent Proportions, Conditional Logistic Regression for Binary Matched Pairs, Marginal Models for Square Contingency Tables, Symmetry, Quasi-symmetry, and Quasi independence, Measuring Agreement between Observers, Bradley Terry Model for Paired Preferences, Marginal Models and Quasi-symmetry Models for Matched Sets.
Analyzing Repeated Categorical Response Data
-Comparing Marginal Distributions: Multiple Responses, Marginal Modeling: Maximum Likelihood Approach, Marginal Modeling: Generalized Estimating Equations Approach, Quasi likelihood and Its GEE Multivariate Extension Details, Markov Chains: Transitional Modeling.

Reference Book:

  • Agresti A. (2012).Categorical Data Analysis. 3rd Edition. Wiley

 

Credits 4
Pre-requisite

AST- 510
Description

  • Review on Parametric Regression Models for Lifetime Data: Introduction, graphical methods for model selection, inference for log-location scale models, and extension of log-location scale models.
  • Semi-parametric Multiplicative Hazards regression Model: Introduction, estimation of parameters, inclusion of strata, time-dependent covariates, residuals and model checking, methods for Grouped or discrete lifetimes, related topics on the Cox model.
  • Rank-Type Procedures for Log-Location-Scale models: Rank tests for comparing distributions, estimation for semi-parametric accelerated failure time models.
  • Multiple Modes of Failure: Basic characteristics of model specification, likelihood functions formulation, nonparametric methods, parametric methods, semi-parametric methods for multiplicative hazards model.
  • Logistic regression, Goodness of fit test, Test of fit of regression model: Location-scale regression models.
  • Analysis of Correlated Lifetime Data: Introduction of regression models for correlated lifetime data, representation and estimation of bivariate survivor function.

References:

  1. Lawless, J.F. (2003). Statistical Models and Methods for Lifetime Data. 2nd Edition. Wiley
  2. Kalbfleisch, J.D. and Ross, L.P. (2002). The Statistical Analysis of Failure Time Data, 2nd Edition. Wiley
Credits 4
Pre-requisite

AST- 511
Description

  1. Review of Analysis of variance (ANOVA) for Fixed, Random and Mixed effect models with and without Interaction.
  2. Analysis of co-variance: one–way and two–way classifications. Estimation of main effects, interactions and analysis of 2k factorial experiment in general with particular reference to k = 2, 3 and 4 and 32 factorial experiments. Multiple comparisons, Fisher LeAST- Significance Difference (L.S.D) test and Duncan’s multiple range test (DMRT).
  3. Total and partial confounding in case of 23, 24 and 32 factorial designs. Concept of balanced partial confounding. Fractional replications of factorial designs – one-half replication of 23& 24 design, one-quarter replication of 25& 26 Split–plot design.
  4. Balanced incomplete block design (BIBD) – parametric relations, intra-block analysis, recovery of inter-block information. Partially balanced incomplete block design with two associate classes PBIBD (2) – Parametric relations, intra block analysis. Simple lattice design and Youden-square design
  5. Concept of Response surface methodology (RSM), the method of steepest ascent. Response surface designs. Design for fitting first – order and second – order models. Variance of estimated response. Second order rotatable designs (SORD), Central composite designs(CCD): Role of CCD as an alternative to 3k design, Annotatability of CCD

 References:

  1. Sahai, H. and Ageel, M.I. (2000). The Analysis of Variance: Fixed, Random and Mixed Models. 2000th Birkhauser
  2. Christensen, R. (1996). Analysis of Variance, Design and Regression. Chapman and Hall/CRC, London
  3. Rencher, A.C. and Schaalje G.B. (2008). Linear Models in Statistics.2nd Edition Wiley -Interscience, New York
  4. Sahai, H. and Ojeda, M.M. (2013). Analysis of Variance for Random Models. 1st Edition, Birkhauser, Boston
  5. Montagomery, D. C. (2012): Design & Analysis of Experiments. 8th Wiley
  6. Dean A.M. and Voss D (2001). Design and analysis of experiments. Corrected Edition. Springer.

 

Credits 4
Pre-requisite

AST-512
Description

Understanding Environmental Pollution:  Pollution and its Importance, Why does Pollution happen, Pollutant Sources, Detail Study of Air and Water Pollution, Global Climate Change Environmental Standards: Concept of Environmental Standards, Statistically Verifiable Ideal Standard (SVIS), Guard Point Standards, Standards along Cause-Effect Chain.

Stochastic Process in Environment: Applications of Bernoulli, Poisson and Normal Process to Environmental problems.

Environmental Sampling: Network Sampling, Composite Sampling, Ranked-set Sampling,  Quadrat sampling, Capture-Recapture sampling, Transect sampling, Line Transects and variable circular plots, Density Estimation, Method of line transects, Spatial distribution and prediction, Spatial Point process models and methods.

Diversity: Measurement of diversity, Different diversity indices.

Diffusion and Dispersion of Pollutants: Wedge Machine, Particle Frame Machine, Plume Model.

Dilution of Pollutants: Deterministic Dilution, Theory of Successive Random Dilution (SRD), Application of SRD to Environmental Phenomena: Air Quality, Indoor Air Quality, Water Quality, Concentrations of Pollutants in Soils, Plants and Animals, Concentration in Food and Human Tissue.

Statistical Theory of Rollback: Predicting concentrations after Source Control, Correlation, Previous Rollback Concepts, Environmental Transport Models in Air and Water.

Environment and economics: Theory of Environmental Externalities, Coase Theorem, Environmental Welfare analysis, Trade and Environmental policy, Resource allocation over time, valuing the environment, Cost-benefit analysis, Allocation of resources, Renewable and Non-renewable resources.

 

Text Book

  • Barnett, V. (2004). Environmental Statistics: Methods and Applications, John Wiley and Sons, New York.

References

  1. Bryan, F. J. (2000). Statistics for Environmental Science and Management. 1st Edition, Chapman and Hall/ CRC, Press
  2. Millard, S.P. and Neerchal, N.K. (2000). Environmental Statistics Using S-Plus. Chapman and Hall/CRC Press
  3. John, T. (2003). Practical Statistics for Environmental and Biological Scientists. John Wiley and Sons, New York
  4. Robert, H. (1990).Spatial Data Analysis in the Social and Environmental Sciences. Cambridge University Press, Cambridge Articles from different Journals.

 

Credits 3
Pre-requisite

AST- 513
Description

  1. A methods curse in statistic aspects of reliability. Topics include: application of normal, lognormal, exponential, weibul models to reliability problem; censored; probability and hazard plotting; series system and multiple failure models, maximum likelihood estimation; introduction to accelerated life models and analysis.
  2. Coherent Systems: Reliability concepts – Systems of components. Series and parallel systems – Coherent structures and their representation in terms of paths and cuts, Modular decomposition.
  3. Reliability of coherent systems – Reliability of Independent components, association of random variables, bounds on systems reliability and improved bounds on system reliability under modular decomposition.
  4. Life Distribution: Survival function – Notion of aging IFR, DFR, DFRA, NBU and NBUE classes, Exponential distributions and its no-ageing property, ageing properties of other common life distribution, closures under formation of coherent structures, convolutions and mixtures of these cases.
  5. Maintenance and replacement policies, relevant renewal theory, availability theory, maintenance through spares and repair.
  6. Reliability estimation: Estimation of two and three parameter Gamma, Weibull and log normal distributions

References

  1. Barlow, R.E. and Proschen, F. (2007). Statistical Theory of Reliability and life testing. 2nd Halt, Reinhart and Winston Inc
  2. Barlow and Proschen (1996). Mathematical Theory of Reliability. SIAM Edition. John Wiley
  3. (2010). Reliability Engineering, 10th Edition,Tata Mc Graw Hill.
  4. J. (1980). Statistical Analysis of Reliability and like testing Models. Marcel Decker, New York.
  5. Sinha, S.K., and Kale, S.K., (1980). Life testing and Reliability Estimation. Wiley Eastern.

 

Credits 3
Pre-requisite

AST- 514
Description

Epidemiologic Research, Etiologic Research, Experiments, Quasi Experiments, Observational Studies, lifetime distribution, continuous model, discrete model, hazard function, Survival function, regression models, Subject selection, Methods of observation, Ratio measures, Difference measures, Basic Designs: Cohort study, cross-sectional study, case-control study, Hybrid designs, incomplete designs

Measures of Disease Frequency: Describe the key aspects of measuring disease occurrence, Basic incidence measures; risk and rate, Estimation of average rates, Estimation of risk, Prevalence measures, Mortality measures, mathematical relationship between the measures of diseases frequency, provide examples of commonly used measures of diseases frequency in public health.

Identifying Non-causal Associations, Confounding: The nature of association between the confounder, the exposure and the outcome, risk factors, single risk factor confounding; Confounding involving several risk factors; definition of joint confounding, variable selection, Assessing the presence of confounding, control of confounding, Additional issue related to confounding.

Selection Bias and Information Bias: General Formulation, Direction of selection bias, Example of selection bias, Examples of misclassification in only the outcome variable, general formulation of misclassification bias, independent misclassification of both exposure and disease.

Multivariate Analysis in Epidemiology: Stratification and Adjustment techniques to Disentangle confounding, Adjustment Methods based on stratification, Multiple Regression Techniques for Adjustment, Alternative approaches for the control of confounding, Incomplete adjustment: Residual Confounding, over adjustment, Logistic regression analysis: follow-up and case-control studies, logistic modeling: Application to real life data, Applications of logistic regression with interaction, using unconditional ML estimation.

Epidemiological issues in the interface with public health policy: Introduction, Causality: Application to public health and health policy, Decision tree and Sensitivity analysis, Meta-Analysis, Publication bias.

Reference:

  1. Kleinbaum, D.G., Kupper, L.L. and Morgenstern, H. (1982). Epidemiologic Research: Principles and Quantitative Methods.
  2. Rothman, K.J., Lash, T.L. and Greenland, S. (2012). Modern Epidemiology. 3rd Lippincott Williams and Wilkins, USA.
  3. Szklo, M. and Nieto, F.J. (2012).Epidemiology, Beyond the Basics. 3rd Edition, Jones & Bartlett Learning.
  4. Lawless, J.F. (2002). Statistical Models and Methods for Lifetime Data. 2nd Wiley-Interscience.

 

Credits 3
Pre-requisite

AST- 515
Description

Methods of Population Analysis: Rates, Ratios, Proportions, Percentages, Person, Months/Year, Incidence, Prevalence, Rates of Population Growth, Cohort and cross-sectional indicators, Crude rates and standardized methods, Methods of Population projections, Inter-censal/ postcensal estimates of population.

Population Aging:  Elderly Situation, Aging Index, Support Ratio Index, Care Index, Elderly Situation in Bangladesh, Components (Elements) of Aging Policy in Bangladesh, Goals and Objectives of Aging Policy in Bangladesh.

Gender Preference: Family Size, Ideal Family Size, Sex Preference of Family Size, Factors Affecting Sex Preference in Bangladesh, Relationship between Actual Fertility and Ideal Fertility, Fertility of Spacers and Limiters and their effect, Effect of under five mortality or infant mortality on Desired Family Size.

Decomposition of Change in TFR between two Time Periods: Bongaart’s Model, Target setting by Bongaarts Model, Relationship between Fertility and Contraceptive use.

Population Stabilization: Population Stabilization, Tempo Effect, Quantum Effect, Implication of Population Stabilization if Replacement Fertility is not Achieved, Population Momentum, Reduction of Population Momentum, Factors to be Considered in Reduction Population Momentum.

Demographic Benefits: Achieved Replacement Fertility in Time, Its Benefit in falling Fertility, Demographic Window/Bonus: Implication of Macro Economic Growth.

Population Policies and in Bangladesh: History of growth of population in Bangladesh; Implications of the growth of population in Bangladesh; Population policy in Bangladesh; Level, trends and determinants in fertility, mortality and migration in Bangladesh; Interrelationship between population and development; Future prospects of population and population control in Bangladesh; Aged and aging of population in Bangladesh;

References:

  1. Shryock et al (2004). The methods and materials of demography. Volume I and II.U.S, Department of Commerce Publication.
  2. Chiang, C. L. (1984). The Life Table and Its Applications. Krueger Pule, John Wiley, New York.
  3. Bongaarts, J. and Potter, R.G. (1982). Potter Fertility. Biology and Behaviour: AnAnalysis of the Proximate Determinants of Fertility. Academic Press, Sandiego, California.
  4. Colin, N. (1988). Methods and Models in Demography. Belhaven Press, London.
  5. Selected articles from Population Studies, Demography. Population and Development Studies in Family Planning etc.
  6. SmithD, KeyfitzN. (2011): Mathematical Demography. Springer
Credits 3
Pre-requisite

AST- 516
Description

  1. Multicollinearity: nature, detection, consequence and remedy of multicollinearity
  2. Autocorrelation 
  3. Heteroscedasticity
  4. Model Specification: Consequences of under and over specification, model selection criteria
  5. Estimation and application of Cobb-Doglas production function
  6. Simultaneous equation models :
    • Simultanious equation bias
    • Inconsistance of OLS estimations
    • Types and rules of identification
    • Estimation of simultanious estimation methods: Methods of idirect leAST- square(ILS) and two stage least square(2SLS)

       7.Non-Linear regression:

  • Least Square Estimation,
  • Estimating the Parameter: Response surface methodology, Semilogarithm
  • Time series Econometrics: Stationarity, Unit roots and co-integration, Spurious regression, Dynamic Econometrics model, Distributed lag models.

     8. Panel Data Models:

  • Fixed Effects
  • Random Effects
  • Dynamic Model

References:

  1. H. Greene (2011). Econometric Analysis. 7th Edition. Prentice Hall.
  2. M. Wooldridge (2010). Econometric Analysis of Cross Section and Panel Data. 2nd Edition. The MIP Press.
  3. M Verbeek (2000). A guide to Modern Econometrics. 3rd Edition, John Wiley & Sons

 

Credits 3
Pre-requisite

AST- 517
Description

  • Simple and multiple regression models;
  • point estimation in the general linear model,
  • projection operators,
  • estimable functions and generalized inverses;
  • Tests of general linear hypotheses; Diagnostics and Remedial Measures.
  • power;
  • Matrix Approach of the general linear model
  • Quadratic Forms and Their Distributions,
  • General Linear Models, General Framework,
  • Least Squares,
  • Properties of Estimators,
  • Gauss-Markov Theorem,
  • analysis of variance (ANOVA)
  • analysis of covariance models (ANOCOVA)
  • Interval Estimates of Parameters, Testing of Hypothesis, Diagnostics and Remedial Measures
  • Generalized Least Squares,
  • Extra Sums of Squares,
  • Estimation and Hypothesis Testing for Full Rank and Less than Full Rank Models, Model Selection Criteria,
  • fixed, random, and mixed effects model;
  • Correlation;
  • methods for simultaneous inference ;
  • residual analysis and checks of model adequacy

Text books 

  1. Rencher, A.C. (2000). Linear Models in Statistics. Wiley, New York
  2. Seber, G.A.F. (1977). Linear Regression Analysis. Wiley, New York

 

References

  1. Guttman, I. (1982). Linear Models: An Introduction. Wiley, New York.
  2. Draper, N.R. and Smith, H. (1998): Applied Regression Analysis; 3rd Edition, Johan Wiley and Sons
  3. McCullagh, P. and Nelder, J.A. (1989). Generalized Linear Models. Chapman Hall, New York
  4. Ryan, T.P. (1997). Modern Regression Methods. Wiley, New York
  5. Fox, J. (1997). Applied Regression Analysis, Linear Models, and Related Methods. Sage, Thousand Oaks, Ca
  6. Neter, J., Wasserman, W. and Kutner, M.H. (1990). Applied Linear Statistical Models. 3rd Irwin, Boston.
  7. Gujarati, D.N. (2004): Basic Econometrics. 4th Edition. Mc Graw-Hill  Inc
Credits 3
Pre-requisite

AST- 518
Description

  1. Introduction to Epidemiology and Clinical Trials, brief history of clinical trials
  2. Phase I and II clinical trials
    a.Phase I dosing trials, Clinical pharmacology
    b.Phase II clinical trials (screening and feasibility): Review of confidence intervals, Gehan’s two-stage design, Simon’s two-stage sequential design
  3. Phase III clinical trials fundamentals
    a.Issues to consider before designing a clinical trials
    b.Ethical Issues
    c.Randomized clinical trials
  4.  Randomization
    a.Design based inference
    b.Fixed allocation randomization
    c.Adaptive randomization
    d.response adaptive designs
  5. Additional issues in Phase III clinical trials
    a.Single blind and double blind
    b.Use of placebo controlled trials
    c.The protocol document
  6. Sample size calculations
    a.Test for equality – Continuous: T-test for two-sample comparison, ANOVA- F-tests
    b.for K-sample comparisons
    c.Test for equality – Categorical: Proportions test for two-sample comparisons, Arc-sin square root transformation to stabilize variance, Chi-square test for K-sample comparisons.
    d.Test for equivalency
  7. Causality, non-compliance and intent-to-treat
    a.Causality and counterfactual random variables
    b.Noncompliance and intent-to-treat analysis
    c.A causal model with noncompliance
  8. Survival analysis in Phase III clinical trials
    a.Distribution of time to event
    b.Life-table methods and Kaplan-Meier estimator
    c.Log rank tests for two and K-sample comparisons
    d.Power and sample size considerations
    e.Multiple comparisons
  9. Early stopping of clinical trials
    a.General issues in monitoring clinical trials
    b.Information based design and monitoring
    c.Type I error – equal increments of information
    d.Choice of boundaries: Pocock boundaries, O’Brien-Fleming boundaries
    e.Power and sample size calculation: Inflation factor, Information based monitoring,
    f.Average information, Group sequential tests with equal increments of information

 References:

  1. Steven P. (2005). Clinical Trials: A Methodologic Perspective. 2nd Edition. Wiley Interscience
  2. Friedman, L.M., Furberg, C.D. and De Mets, D.L. (1999). Fundamentals of Clinical Trials. 3rd Edition .Springer

 

Credits 3
Pre-requisite

AST- 519
Description

Review of Survival Models, Life tables and Selection, Multiple State Models, Joint Life and last Survivor benefits

Pension mathematics: Summary, Salary Scale Function, Valuation of Benefits, Service table

Yield curves and Non-diversifiable Risk: Yield Curve, valuation of Insurances and Life annuities, Diversifiable and non-diversifiable Risk, Monte Carlo Simulation

Emerging Costs for Traditional Life Insurance: Introduction, profit testing a term insurance policy, Profit testing Principles, Profit measures, Profit testing Multiple State Models Simulation: The Inverse Transform method, The Box Muller method, The Polar method

References:

  1. Dickson, D.C.M. Hardy, M.R. and Waters, H.R (2013). Actuarial mathematics for life contingent risks. 2nd Cambridge University Press.
  2. Benjamin, B. and Pollard, J.H. (1993). The Analysis of Mortality and other Actuarial Statistics. 3rd Institute and Faculty of Actuaries.
  3. Jordan, C.W. (1975). Life Contingencies. 2nd Edition. Chicago: Society of Actuaries

 

Credits 3
Pre-requisite