bos: 03.04.2018 department of statistics ...apply the python language for statistical data analysis...

Appendix: B

BOS: 03.04.2018

DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH

ALIGARH MUSLIM UNIVERSITY

M.A./M.Sc. I Semester (Statistics)

Course Code: STM1001

Real and Complex Analysis

Credit: 04 Max. Marks: 30+70=100

Course objectives: To understand the basic and advanced elements of real and complex analysis.

Course outcomes: On successful completion of this course, the students will be able to

Demonstrate an understanding of the concepts of real and complex number systems.

Apply the techniques of real and complex analysis in statistical applications.

Syllabus

Unit I: Recap of elements of set theory, introduction to real numbers, open and closed intervals,

bounded and unbounded set, supremum and infimum, algebraic structure of real numbers, the

extended real numbers, countable and uncountable sets, limit points and isolated points of a set,

open and closed sets, closure of a set, compact set, Bolzano-Weierstrass theorem.

Unit II : Concept of sequence, Convergent, divergent and bounded sequences, limit inferior and

limit superior, Cauchy sequence, monotonic increasing and decreasing sequences, infinite series,

sequence of partial sums and convergence of infinite series. real valued function, continuous

functions, uniform continuity of functions.

Unit III: Differentiability of functions, monotonic increasing and decreasing functions, Rolle’s

theorem, mean value theorems, Taylor’s theorem with various forms of reminders, maxima and

minima of functions, power series and radius of convergence, Riemann integral and Riemann

Stieltjes integral, differentiation under integral sign.

Unit IV: Concept of complex numbers, geometric interpretation of complex numbers, algebraic

properties, properties of moduli, complex conjugates, polar and exponential forms, power and roots

of a complex number, functions of complex variables, limits, continuity and derivatives of complex

valued functions, Cauchy-Riemann equations, analytic functions.

Books Recommended:

1. Rudin Walter (1976): Principles of Mathematical Analysis, 3rd

Edition, McGraw-Hill

Education. New York.

2. Bartle, R. G. and Sherbert, D. R. (2007): Introduction to Real Analysis, 4th

Edition, John

Wiley & Sons., USA.

3. Krishnan, V. K. (2004): Fundamentals of Real Analysis, 2nd

Edition, Dorling Kindersley,

Ltd.

4. Malik, S. C. (2017): Principles of Real Analysis, 4th

Edition, New Age International

Publishers.

5. Apostol, T. M. (1974): Mathematical Analysis, 2nd

Edition, Narosa Publishing House.

6. Brown, J. W. and Churchill, R. V. (2014): Complex Variables and Applications, 9th

Edition,

McGraw-Hill Education. New York.

Appendix III B

BOS 05.05.03




Course Code (STM1003) Probability-I


Course objectives: To understand the basic elements of probability theory.


Provide a foundation for understandings of advanced probability courses.

Apply the theory of probability in applications of statistics.

Syllabus Unit I : Random experiment, sample space, field, CT-field, sequences of sets, limsup and limin

of sequences of sets, Measure and probability measure, Lebesgue and Lebesgue-Stieltjes measure,

Measurable and Borel measurable function, Integration of a measurable function w.r.to a

measure, Monotone convergence theorem, Fatous lema and dominated convergence theorem.

Unit II : Random variable (r.v.) and functions of r.v., Probability density and Probability mass

function, Distribution function and its properties, Representation of distribution as a mixture of

distributions, Compound, truncated and mixture distributions.

Unit III : Mathematical expectation and moments, Probability generating function

(PGF), moment generating function (MGF), and characteristic function (CF) and their

interrelationships, Properties of CF. Examples of discrete distributions: Degenerate,

Uniform, Bernaulli, Binomial, Poisson, Geometric, Negative Binomial and Hyper

geometric distribution, Convergence of distribution function.

Unit IV: MGF and CF for continuous r.v., Inversion theorem, Examples of continuous

distributions: Uniform, Normal, Exponential, Gamma, Beta, Weibull, Pareto,

Laplace, Lognormal, Logistic and Log-Logistic distribution.

Books Recommended:

1. Ash, Robert (1972): Real Analysis and Probability, Academic Press. 2. Bhat, B. R (1981): Modern Probability Theory, Wiley Eastern Ltd., New Delhi.

3. Rohatgi, V. K. (1988): An Introduction to Probability and Mathematical Statistics, Wiley, Eastern Limited.

Appendix: B

BOS 03.04.2018

DEPARTMENT OF STATISITICS & OPERATIONS RESEARCH

ALIGARH MUSLIM UNIVERSITY ALIGARH

M.A./ M.Sc. I Semester (Statistics)


Linear Algebra

Credit: 4 Max Marks: 30+70=100

Course objectives: To introduce the theory of linear algebra in the scenario of statistics.


Describe the fundamentals of linear algebra

Apply the concepts and results of linear algebra in statistical problems.

Syllabus Unit I: Vector spaces, Linear combinations, Spanning sets, Subspaces, Linear dependence and

independence, Basis and dimensions, Inner product spaces, Gram-Schmidt orthogonalization

process, Orthinormal basis.

Unit II: Linear transformations, Kernel and Image of linear transformations. Algebra of matrices,

Types of square matices, Elementary operations and Row- reduced echelon form, Inverse of a

matrix, Rank of matrices, Kronecher product of matrices.

Unit III: System of linear homogeneous and non-homogeneous equations, Condition for

consistency, Eigen values and Eigen vectors of matrices, Matrix representation of a linear operator,

Characteristic polynomials and characteristic equations, Eigen values and Eigen vectors of linear

operator, Cayley Hamilton Theorem.

Unit IV: Minimal polynomials, Block matices, Diagonal forms, Jordan canonical forms, Quadratic

forms, Congruence of quadratic forms, reduction of quadratic form, Classification of quadratic

forms.

Books Recommended:

Banerjee, S. and Roy, A.( 2014): Linear Algebra and Matrix Analysis for Statistics. Chapman and

Hall/CRC Press.

Hoffman, K. and Kunze, R. (1971). Linear Algebra (Second edition). New Jersey: Prentice Hall.

Rao, C.R. (1973). Linear Statistical Inference and its Applications (Second Edition). New York:

John Wiley & Sons Inc.

Searle S.R. (1982): Matrix Algebra useful for Statistics. John Wiley and Sons, Inc.

Appendix B

BOS 03.04.2018

DEPARTMENT OF STATISTICS& OPERATIONS RESEARCH


M.A./ M.Sc. I Semester (Statistics)


Statistical Process and Quality Control


Course Objectives: To introduce the basic and advance concepts of statistical quality control.

Course Outcomes: On successful completion of this course, the students will be able to

Describe the techniques of statistical quality control.

Apply the methodologies of SQC to improve the quality of production.

Syllabus Unit I: Concepts of quality, Costs in Quality, Causes of variations, Quality risks, natural tolerance

and specification limits. Control charts for variables ( ,,, SRX ) and attributes (p, np, c, u).

Control charts for regular monitoring of small shifting of mean: Moving range and Average,

exponentially weighted moving average and Cusum.

Unit II: Capability indices Cp, Cpk, and Cpm, estimation of the proportion of defectives (rework and

scrap), confidence intervals and tests of hypothesis relating to capability for normally distributed

characteristics. Quality loss functions, Estimation of quality loss.

Unit III: Taguchi loss function, equal and unequal N-type, L-type and S-type loss functions.

Acceptance sampling plans, rectifications plan, producer’s and consumer’s risks, Acceptance

sampling plans for attribute inspection; single, double and their properties (OC curves, ATI, AOQ,

ASN).

Unit IV: Multiple, Sequential sampling plans. Acceptance Sampling procedure for inspection by

variables: Single sampling plan for one sided and two sided specification with known and unknown

S.D. lot by lot inspection plan. Use of Design of Experiments in SPC: signal and input variables,

full factorial experiments, 2k full factorial experiments, 2

2 and 2

3 construction designs and analysis

of data.

Books recommended:

1. Montgomery, D. C. (2012): Introduction of Statistical Quality Control; Wiley.

2. Montgomery, D. C. (2009): Design and Analysis of Experiments; Wiley. 3. G. Schilling (1982): Acceptance Sampling in Quality Control; Marcel Dekker.

4. Amitava Mitra (2016): Fundamentals of Quality Control and Improvements; John Wiley.

5. John S. Oakland (2008): Statistical Process Control; Elsevier.

6. Kaoru Ishikawa (1992): Introduction to Quality Control; Chapman and Hall.

DEPARTMENT OF STATISTICS & OPERATIONS

RESEARCH ALIGARH MUSLIM UNIVERSITY ALIGARH


Course Code (STM 1012)

Statistical Methods


Course objectives: To introduce the basis and advanced concepts of non-parametric inference.


Describe the techniques and methods of non-parametric inference.

Apply the methodologies of non-parametric inference in data analysis.

Syllabus

Unit I: Order Statistics: Discrete & continuous joint and marginal distribution of order

statistics, distribution of range. Distribution of censored sample. Example based

on continuous distributions.

Unit II: Confidence intervals for distribution quantiles, tolerance limits for

distributions. Asymptotic distribution of function of sample moments. U-Statistics,

Transformation and Variance stabilizing results.

Unit III : Non-parametric location tests: One sample problem: Sign test, signed rank test,

Kolmogrov-Smirnov test, Test of independence (run test). Two sample problem: Wilcoxon-

Mann-Whitney test, Median test, Kolmogrov-Smirnov test, run test.

Unit III : Non-parametric scale tests: Ansari-Bradely test, Mood test, Kendall's Tau test,

test of randomness, consistency of tests and ARE. Books recommended:

1. Gibbons, J.D. (1971): Non-parametric Statistical Inference, Mc Graw Hill Inc.

2. Hogg, R.V. & Raise, A.I. (1978): Introduction to mathematical satsitics, Macmillan

Pub. Co. Inc.

Appendix B/1

B.O.S- 30.05.2019

DEPARTMENT OF STATISTICS AND OPERATIONS RESEARCH

ALIGARH MUSLIM UNIVERSITY, ALIGARH

M.A/M.Sc.(Statistics)

I-Semester

Course Code-STM1022

Data Analysis with Python


Course objectives: To introduce the basis and advanced elements of the Python language.


Demonstrate the understanding of Python language.

Apply the Python language for statistical data analysis and graphics.

Syllabus Unit I: Introduction to Python- Python data structures, data types, indexing and slicing, vectors,

arrays, developing programs, functions, modules and packages, data structures for statistics, tools

for statistical modeling, data visualization, data input and output.

Unit II: Display of Statistical data with Python- Univariate and multivariate data, discrete and

continuous distributions: binomial, Poisson, normal, Weibull. Sampling distributions: t, chi-square

and F.

Unit III: Hypothesis testing with Python- Test for means: t test for single and two samples,

Wilcoxon and Mann-Whitney test, test for categorical data, one proportion and frequency tables,

chi-square test for independence, relation between hypothesis and confidence intervals, one- and

two -way ANOVA.

Unit IV: Statistical Modeling with Python-Correlation and Regression coefficients, simple and

multiple regression analyses, model selection criteria, bootstrapping, generalized linear models.

References

1. Haslwanter, T. (2016): An Introduction to Statistics with Python: with Applications in the Life

Sciences, Springer.

2. Sheppard, K. (2018): Introduction to Python for Econometrics, Statistics and Data analysis,

Oxford University press.



M.A/M.Sc. (Statistics)

I-Semester

Course Code-STM1071

Lab. Course – Based on STM1004, STM1011, STM1012,


Appendix B/2

BOS 30.05.2019



M.A/M.Sc.(Statistics) I-Semester

Course code-STM1072

Lab. Course – Data Analysis with SPSS


Course objectives: Main objective of the course is to train the students in statistical data

analysis using SPSS software package.


Describe the elements of data analysis.

Solve the real life problems using statistical software SPSS

Syllabus

Unit I: Basics: Import and export of data files, recoding, computing new variables, selection of

cases, splitting and merging of files. levels of measurement (types of data), summarizing variables

using frequencies and descriptive statistics, bar charts, histograms and box plots, computation of

simple, multiple, partial and rank correlation coefficients.

Unit II: Regression analysis: fitting of linear, parabolic, cubic and exponential models, multiple

linear regression, variable selection, residual analysis for model adequacy, detection of outliers and

influential observations.

Unit III: Testing of Hypothesis: Parametric tests; Tests based on t, F and chi square statistics.

Nonparametric tests; run test for randomness, sign test for location, median test, Mann-Whitney-

Wilcoxon test, Kolmogorov-Smirnov test - one and two sample problems.

Unit IV: Analysis of variance: Analysis of one way and two way data, analysis of CRD, RBD and

LSD, analysis 23, 2

4, 3

2 and 3

3 factorial experiments, multiple comparison tests.

Books Recommended:

1. John MacInnes, An Introduction to Secondary Data Analysis with IBM SPSS Statistics, Sage

2017.

2 Marija Norusis, The SPSS Guide to Data Analysis, 1991.

3. Stephen A. Sweet, and Karen Grace-Martin, Data Analysis with SPSS: A First Course in

Applied Statistics, 4th Edition, Pearson, 2012.

4. Pallant, Julie,SPSS Survival Manual, 4th Ed, McGraw-Hill, 2010.

5. Cronk, Brian, How to Use SPSS: A Step-By-Step Guide to Analysis and Interpretation,5th Ed.,

2008

https://surveyresearch.weebly.com/mcinnes-2017.html

http://www.norusis.com/about.php

https://surveyresearch.weebly.com/sweet-and-grace-martin-2010.html

https://surveyresearch.weebly.com/sweet-and-grace-martin-2010.html

Appendix:B

BOS: 03.04.2018




II-Semester

Course Code-STM-2001 Probability II


Course objectives: To Introduce the advanced concepts of probability theory.


Describe the advanced techniques of Probability theory including LLN and CLT.

Apply the results of advanced Probability in statistical theory

Syllabus

Unit I : Derivation of central ;c2, t and F distributions. Ideas of non-central

distributions. Multidimensional r.v., its pdf/pmf and cdf. Bivariate distributions.

Joint, Marginal and conditional distributions, conditional moments and their

properties, covariance and correlation between two r. v. Unit II : Bivariate and multivariate normal, multinomial and multi-hypergeometric

distributions, Distributions of functions of r. vs (discrete and continuous).

Unit III : Chebyshev, Markov, Jensen, Liapunov, Holder, Minkowski and Kolmogrov

inequality, various models of convergence and their interrelationships Convergence of

rational Functions of r.vs. (Cramer).

Unit IV: Continuity theorem (Levy-Cramer Statements only), Kolmogrov's three

series criterion, Weak and strong law of large numbers, Central limit theorems in De

Moivre-Laplace, Lindberg-Levy and Liapunov's versions. 0-1 law of Borel and

Kolmogrov.

Books Recommended:

1. Ash, Robert (1972): Real Analysis and Probability, Academic press.

2. Bhat, B.R (1981 ): Modern Probability Theory, Wiley Eastern Ltd. New Delhi.

3. Rohatgi, V.K. (1988): An Intoduction to Probability and Mathematical Statistics,

Wiley Eastern Limited

Appendix:B

BOS: 03-04-2018



M.A./M.Sc. (Statistics/Operations Research)

II Semester

Course Code: STM/ORM2002

Stochastic Processes


Course objectives: To introduce the concepts of stochastic processes.


Describe the techniques of stochastic processes.

Apply the concepts and results of stochastic process in the real life scenario, including

queuing theory, branching process, MCMC, etc.

Syllabus

Unit I: Introduction to stochastic processes, classification of stochastic processes, mean,

correlation, covariance and auto-correlation functions, stationary and wide-sense stationary

processes, Markov processes, martingale process, Markov chains: definition, transition graphs,

transition probability matrix, order of a Markov chain, Chapman-Kolmogorov equation.

Unit II : Classification of states and chains: transient, persistent and ergodic states, evaluation of n-

step transition probability matrix through spectral decomposition, stationary distribution of the

chain, continuous time Markov processes and their properties, Poisson process and its applications.

Unit III: Simple birth process, simple birth and death process, Yule-Furry process, introduction to

branching process, properties of generating functions of branching processes, probability of

extinction, distribution of the total number of progeny, one-dimensional and two-dimensional

random walk, gambler's ruin problem.

Unit IV: Statistical inference for Markov chains: maximum likelihood estimation of transition

probability matrix, tests of hypothesis about transition probability matrix, introduction to renewal

process, distribution of number of renewals, expected number of renewals, renewal function,

renewal integral equation, stopping time, Wald’s equation, renewal theorem.

Books Recommended:

1. Medhi, J. (1994): Stochastic Processes, 2nd

Edition, New Age International Limited.

2. Ross, S. M. (2008): Stochastic Processes, 2nd

Edition, John Wiley & Sons, Inc., New

York.

3. Bailey, N. T. (1965): The Elements of Stochastic Processes, John Wiley & Sons, Inc.,

New York.

4. Sundarapandian, V. (2009): Probability, Statistics and Queueing Theory, PHI Learning

Private Limited.

5. Taylor, H. M. and Karlin, S. (1998): An Introduction to Stochastic Modeling, 3rd

Edition,

Academic Press.

Appendix III B

BOS 05.05.03

DEPARTMENT OF STATISTICS & OPERATIONS

RESEARCH ALIGARH MUSLIM UNIVERSITY ALIGARH

M.A. /M.Sc II Semester (Statistics)

Course Code-STM2003

Sample Surveys

Credit: 4 Max Marks: 30+70 =100

Course objectives: To introduce the concepts of sample surveys and designs.


Describe the methods of sample surveys.

Apply the methods in data collections and data analysis.

Syllabus

Unit I: Estimation of population mean, total and proportion in SRS and Stratified

sampling. Estimation of gain due to stratification. Ratio and regression methods of

estimation. Unbiased ratio type estimators. Optimality of ratio estimate .Separate and

combined ratio and regression estimates in stratified sampling and their comparison.

Unit II : Cluster sampling: Estimation of population mean and their variances based on

cluster of equal and unequal sizes. Variances in terms of intra-class correlation

coefficient. Determination of optimum cluster size.Varying probability sampling:

Probability proportional to size (pps) sampling with and without replacement and related

estimators of finite population mean.

Unit III : Two stage sampling: Estimation of population total and mean with equal and

unequal first stage units. Variances and their estimation. Optimum sampling and sub-

sampling fractions (for equal fsu's only).Selection of fsu's with varying probabilities and

with replacement.

Unit IV: Double Sampling: Need for double sampling. Double sampling for ratio and

regression method of estimation. Double sampling for stratification. Sampling on two

occasions. Sources of errors in surveys: Sampling and non-sampling errors. Various

types of non -sampling errors and their sources .Estimation of mean and proportion in

the presence of non-response. Optimum sampling fraction among non-respondents.

Interpenetrating samples. Randomized response technique.

Books Recommended:

1. Cockran, W.G., (1977): Sampling Techniques, 3rd edition, John Wiley.

2. Des Raj and Chandak (1998): Sampling theory, Narosa.

3. Murthy, M.N. (1977): Sampling theory and methods. Statistical Publishing

Society, Calcutta.

4. Sukhatme et al. (1984): Sampling theory of surveys with applications, Lowa state university press and ISAS.

5. Singh, D. and Chaudary, F.S. (1986): Theory and analysis of sample survey

designs. New age international publishers

Appendix III B

B.O.S. 05.05.03



M.A. /M.Sc. II Semester (Statistics)

Course Code-STM2011

Linear Models and Regression Analysis


Course objectives: To introduce basic and advance concepts of general linear model.


Describe the concepts of linear models in real applications of statistics modeling

Apply concepts of linear models to illustrate its application areas like design of

experiments, econometrics, survival analysis and demography.

Syllabus

Unit I : Linear Estimation: Gauss-Markov linear Models, Estimable functions, Error

and Estimation Spaces, Best Linear Unbiased Estimator (BLUE), Least square

estimator, Normal equations, Gauss-Markov theorem, generalized inverse of matrix

and solution of Normal equations, variance and covariance of Least square estimators.

Unit II : Test of Linear Hypothesis: One way and two way classifications. Fixed,

random and mixed effect models (two way classifications only), variance components.

Unit III : Linear Regression: Bivariate, Multiple and polynomials regression and

use of orthogonal polynomials. Residuals and their plots as tests for departure from

assumptions of fitness of the model normality, homogeneity of variance and detection of

outlines. Remedies.

Unit IV : Non Linear Models: Multi-collinearity, Ridge regression and principal

components regression, subset selection of explanatory variables, Mallon's Cp Statistics.

Book Recommended:

1. Goon, A.M., Gupta, M.K. and Dasgupta, B. (1987): An Outline of Statistical

Theory, Vol. 2, The World Press Pvt. Ltd. Culcutta.

2. Rao, C.R. (1973): Introduction to Statistical Infererence and its Applications,

Wiley Eastern.

3. Graybill, F.A. (1961): An introduction to linear Statistical Models, Vol. 1, McGraw

Hill Book Co. Inc.

4. Draper, N.R. and Smith, H (1998): Applied regression Analysis, 3rd Ed. Wiley.

5. Weisberg, S. (1985): Applied linear regression, Wiley.

6. Cook, R.D. and Weisberg, S. (1982): Residual and Inference in regression,

Chapman & Hall.

-- - -- - -- ------ ------

Appendix:B

BOS: 03.04.2018

Department of Statistics and Operations Research

Aligarh Muslim University, Aligarh

M.A. /M.Sc. II Semester (Statistics)


Data Analysis with R

Credit: 2 Maximum Marks: 30 +70 =100

Course objectives: To introduce the elementary and advanced concepts of R-Language.


Describe statistical modelling using R

Apply these modelling tools in statistical/machine learning.

Interface R and Latex for documentations

Syllabus

Unit I: R language and environment:

Basics of R, naming a data object, R is a functional language, creation of data objects

including vectors, factors, matrices, list and data frames. Extraction from a data object.

Input and output facilities.

Unit II: Univariate analysis:

Descriptive statistics and graphics, probability distributions in R, one -sample and two-

sample tests, power and computation of sample size.

Unit III: Regression modeling:

Analysis of simple and multiple regression models, analysis of variance and analysis of

deviance. Fitting with optim ().

Unit IV: Documentation with R:

Interface of LaTex and R, basics of LaTex, concept of document class, using knitr with

LaTex, Markdown tips, using knitr and Markdown.

Books Recommended:

1. Dalgaard P. (2008). Introductory Statistics with R, Springer.

2. Kleiber C and Zeileis A (2008) Applied Econometrics with R. Springer New York.

3. Lander J. P. (2014). R for Everyone: Advanced Analytics and Graphics, Pearson.

4. Xie, Y. (2015). Dynamic Documents with R and knitr (2nd edition), CRC Press.

.




II-Semester

Course Code-STM2071

Lab. Course – Based on STM2003, STM2011





II-Semester

Course Code-STM2072

Lab. Course – Based on STM2022


Appendix B

BOS 30.07.2016


ALIGARH MUSLIM UNIVERSITY,ALIGARH

M.A. /M.Sc. III Semester (Statistics)

Course Code- STM3001

Statistical Inference-I


Course objectives: To introduce the elementary and advanced concepts of statistical inference.


Describe the concepts of statistical inference.

Apply the statistical inference tools in real data analysis including sample surveys, design of

experiments, and econometrics.

Syllabus Unit I : Criterion of a good estimator - unbiasedness, consistency, efficiency and sufficiency.

Minimal sufficient statistics. Exponential and Pitman family of distributions. Complete

sufficient statistic, Rao-Blackwell theorem, Lehmann-Scheffe theorem, Cramer-Rao

lower bound approach to obtain minimum variance unbiased estimator (MVUE).

Unit II : Maximum likelihood estimator (mle), its small and large sample properties, CAN

and BAN estimators. Most Powerful (MP), Uniformly Most Powerful (UMP) and

Uniformly Most Powerful Unbiased (UMPU) tests. UMP tests for monotone

likelihood ratio (MLR) family of distributions.

Unit III : Likelihood ratio test (LRT) with its asymptotic distribution, Similar tests with Neyman

structure, Ancillary statistic and Basu' s theorem. Construction of similar and

UMPU tests through Neyman structure.

Unit IV: Interval estimation, confidence level, construction of confidence intervals using pivots,

shortest expected length confidence interval, uniformly most accurate one sided

confidence interval and its relation to UMP test for one sided null against one sided

alternative hypothesis.

Books Recommended:

1. Lehmann, E.L. (1983): Theory of Point Estimation, Wiley.

2. Lehmann, E.L. (1986): Testing Statistical Hypothesis, 2nd Ed., Wiley.

3. Rao, C.R. (1973): Linear Statistical Inference and its Applications, Wiley.

4. Rohtagi, V.K. (1976): An Introduction to Probability Theory and Mathematical Statistics,

Wiley.

Appendix B

BOS 30.07.2016



M.A./M.Sc. III Semester(Statistics)

Course Code- STM3002

Design and Analysis of Experiments


Course objectives: To introduce the elementary and advanced concepts of design and analysis of

experiments.


Describe the techniques of design of experiments in real life scenario.

Apply the response surface methodology in different application areas like food science,

quality improvement, etc.

Syllabus Unit I: Analysis of basic designs, relative efficiency, missing plot technique, analysis of

covariance for CRD and RBD. Assumptions of analysis of variance

Unit II: Factorial experiments: 2n, 3

2 and 3

3 systems. Complete and partial confounding,

fractional factorial designs in 2n system along with construction of the design and analysis.

Unit III: Incomplete block designs: Balanced incomplete block designs, simple lattice designs,

split plot designs, strip plot designs, along with construction of the designs and analysis.

Unit IV: Response surface designs: Response surface areas, first and second order designs

blocking in response surfaces, optimal designs for response surfaces.

Books recommended:

1. Wu C.F.J and Hamada. M, (2009). Experiments, Planning, Analysis and Optimization 2nd

Ed, Wiley New York.

2. Montgomery D. C, (2013). Design and Analysis of Experiments, 8th edition, John Wiley &

Sons, New York

3. Oehlert. G. W (2010), A First course in Design and Analysis of Experiments. University of

Minnesota

4. Casella, G, (2008). Statistical Design. Springer

Appendix B

BOS 30.07.2016



M.A./M.Sc. III Semester(Statistics)

Course Code-STM3003

Econometrics and Time Series Analysis


Course objectives: To introduce the elementary and advanced concepts of econometric and time

series analysis.


Describe the concept of econometric modeling.

Apply the econometric tools in the analysis of cross-section, time series and panel data.

Syllabus

Unit I: The General Linear Econometric Model: Ordinary Least Square (OLS) estimation and

prediction. Use of Dummy variables and seasonal adjustment. Generalizes Least Square

(GLS) estimation and prediction. Heteroscedastic disturbances, Pure and Mixed

estimator, Grouping of observations and of equations.

Unit II: Simultaneous Linear Equation Models: Examples, Identification problem. Restrictions on

structural parameters- rank and order conditions. Restrictions on variances and

covariances. Estimation in simultaneous equations model. Recursive systems. 2 SLS

estimators, limited information estimators.

Unit III:Time Series Analysis: Time series as discrete parameter stochastic process. Auto

covariance and autocorrelation function and their properties. Test for trends and

seasonality. Exponential and moving average smoothing. Holt and Winters Smoothing.

Forecasting based on smoothing.

Unit IV:Autoregressive integrated moving average (ARIMA) models: Box-Jenkins models.

Estimation of parameters in ARIMA models. Forecasting, Periodogram and Correlogram

analysis.

Books Recommended:

1. Johnston, J (1984): Econometrics Methods, 3rd edition.

2. Kaytsoyianmis, A. (1979): Theory of Econometrics.

3. Box, G.E.P, Jenkins, G.M. (1976): Time Series Analysis, Forecasting and Control.

4. Kandal & Ord, J.K. (1990): Time Series, 3rd edition.

Appendix B

BOS 30.07.2016



M.A./M.Sc.III Semester (Statistics)

Course Code-STM3004

Multivariate Analysis


Course objectives: To introduce the elementary and advanced concepts of multivariate analysis

tools.


Describe the multivariate analysis tools in relation to univariate tools

Apply multivariate statistical methods in AI, Machine Learning applications.

Syllabus

Unit I: Singular and non-singular multivariate normal distributions, Characteristic function of Np

(µ, ∑) Maximum likelihood estimators of µ and ∑ in Np (µ, ∑) and their independence.

Testing of population mean vector when variance covariance ∑ is known.

Unit II: Wishart distribution: Definition and its distribution, properties and characteristic

function. Generalized variance. Testing of sets of variates and equality of covariance.

Estimation of multiple and partial correlation coefficients and their null distribution,

Test of hypothesis on multiple and partial correlation coefficients

Unit III: Hotelling's T2: Definition, distribution and its optimum properties. Application in

tests on mean vector for one and more multivariate normal population and also on

equality of the components of a mean vector of a multivariate normal population.

Distribution of Mahalanobis's D2.

Discriminate analysis: Classification of observations into one or two or more groups.

Estimation of the misclassification probabilities. Test associated with discriminate

functions.

Unit IV:Principal component, canonical variate and canonical correlation: Definition, use,

estimation and computation. Cluster analysis.

Books Recommended:

1. Anderson,T.W. (1984): An introduction to multivariate statistical analysis. John Wiley.

2. Giri, N.C. (1977): Multivariate statistical inference. Academic Press.

3. Singh, B.M. (2002): Multivariate statistical analysis. South Asian Publishers




III-Semester

Course Code-STM3071

Lab. Course – Based on STM3002, 3003, 3004




M.A/M.Sc. (Statistics)

III-Semester

Course Code-STM3072

Lab. Course – Project

Credit: 4 Max Marks:40+60=100

Appendix:B

BOS: 03.04.2018



M.A./M.Sc. IV Semester (Statistics)


Statistical Inference-II

Credit: 04

Max. Marks: 30+70=100

Course objectives: To introduce the elements of statistical decision theory and Bayesian inference.


Analyze the data through the techniques of statistical decision theory.

Apply the Bayesian inference to real life scenario.

Syllabus

Unit I : Elements of statistical decision problem, formulation of decision problem as two-

person game, non-randomized and randomized decision rules, concept of loss and risk

functions, the conditional Bayes principle, the Bayes risk principle, the minimax principle,

admissibility, least favorable distributions, complete class and minimal complete class.

Unit II: Decision problem for finite parameter space, convex loss function, Rao-Blackwell

theorem for convex loss function, admissible estimators and minimax estimators under

various loss functions, prior distributions: conjugate prior, invariant prior and Jeffrey’s prior,

computation of posterior distributions.

Unit III: Bayes theorem, Bayes estimators under (i) absolute loss function, (ii) squared error

loss function, (iii) ‘0-1’ loss function, (iv) LINEX loss function, (v) entropy loss function,

generalized Bayes estimators, limit of Bayes estimators, Empirical Bayes estimators. Test of

simple hypothesis against a simple alternative from decision theoretic view point.

Unit IV: Bayesian interval estimation, Bayesian testing of hypothesis, Bayes factor for

various types of testing hypothesis problem depending upon whether the null and alternative

hypotheses are simple or composite, Bayesian prediction problems.

Books Recommended:

1. Ferguson, T. S. (1967): Mathematical Statistics, Academic Press, Inc., USA.

2. Berger, J. O. (1985): Statistical Decision Theory and Bayesian Analysis, Springer-Verlag.

3. Liese, F. and Miescke, K. J. (2008): Statistical Decision Theory, Springer.

4. Sinha, S. K. (1998): Bayesian Estimation, New Age International Limited.

5. Srivastava, M. K., Khan, A. H. and Srivastava, N. (2014): Statistical Inference: Theory of

Estimation, PHI Learning Private Limited.

6. Bolstad, W. M. and Curran, J. M. (2017): Introduction to Bayesian Statistics, 3rd

Edition,

John Wiley & Son, Inc., USA.

7. Robert, C. P. (2007): The Bayesian Choice, 2nd

Edition, Springer.

Appendix B

BOS 30.07.2016



M.A./M.Sc.(Statistics/Operations Research)

IV Semester

Course code – STM/ORM4002

Reliability Theory and Survival Analysis


Course objectives: To introduce the elementary and advanced concepts of reliability and survival

analysis.


Describe the basic concepts of reliability and survival analysis in real life scenario.

Apply these tools in application areas like quality improvement, biostatistics, econometrics,

demography. etc.

Syllabus

Unit I: Definition of Reliability function, hazard rate function, pdf in form of Hazard function,

Reliability function and mean time to failure distribution (MTTF) with DFR and IFR. Basic

characteristics for exponential, normal and lognormal, Weibull and gamma distribution, Loss of

memory property of exponential distribution.

Unit II: Reliability and mean life estimation based on failures time from (i) Complete data (ii)

Censored data with and without replacement of failed items following exponential distribution [N

C r],[N B r], [N B T], [N C(r, T)], [N B(r T)], [N C T]. Accelerated testing: types of acceleration

and stress loading. Life stress relationships. Arrhenius – lognormal, Arrhenius-Weibull, Arrhenius-

exponential models.

Unit III: Basis of Survival analysis, Parametric methods - parametric models in survival analysis,

Exponential, Weibull, Delta method in relation to MLE, Fitting of these models in one sample and

two sample problems. Reliability of System connected in Series, Parallel, k-out-of-n.

Unit IV: Regression models in survival analysis. Fitting of Exponential, Weibull, Coxproportional,

hazard models. Model checking and data diagnostics - Basic graphical methods, graphical checks

for overall adequacy of a model, deviance, cox - snell, martingale, and deviance residuals.

Books recommended:

1. Sinha, S.K. (1980): Reliability and life testing, Wiley, Eastern Ltd.

2. Nelson, W. (1989): Accelerated Testing, Wiley.

3. Zacks, S.O.: Introduction to reliability analysis, probability models and statistical, Springer-

Verlag.

4. Meeker and Escobar (1998):

5. Klein, J.P. and Moeschberger, M.L. (2003): Survival Analysis, technique for censored and

trucated data, Springer.

6.Tableman, M. and Kim, J.S. (2004): Survival Analysis Using S, Chapman & Hall/CRC.

7. Lawless J.F. (2003): Models and Methods for life time data, Second edition, Wiley.

8. Collett (2014): Modeling Survival data in medical Research, Third edition, Chapman &

Hall/CRC.

Appendix B

BOS 30.07.2016



M.A./M.Sc. IV Semester (Statistics)

Course Code-STM4003

Demography & Vital Statistics


Course objectives: To introduce the elementary and advanced concepts of demography.


Describe the concepts of demography in real life scenario.

Apply the demographic techniques in various aspects of population studies.

Syllabus Unit I: Population Theories: Coverage and content errors in demographic data, use of

balancing equations and Chandrasekharan-Deming formula to check

completeness of registration data. Adjustment of age data use of Myer and UN

indices Population composition, dependency ratio

Unit II: Measures of fertility: stochastic models for reproduction, distribution of time

to first birth, inter-live birth intervals and of number of births, estimation of

parameters, estimation of parity progression ratio from open birth interval data..

Unit III: Measures of Mortality: Construction of abridged life tables, Distribution of life

table functions and their estimation. Stable and quasi-stable populations,

intrinsic growth rate Models for population growth and their fitting to

population data. Stochastic models for population growth..

Unit IV: Stochastic models for migration and for social and occupational mobility

based on Markov chains. Estimation of measures of mobility. Methods for

population projection. Use of Leslie matrix.

Books Recommended:

1. Keyfitz N., Beckman John A.: Demogrphy Through Problems S-Verlag New York.

2. Bartholomew, D.I. (1982): Stochastic Models for Social Process John wiley.

3. Benjamin, B. (1969): Demography Analysis, George, Allen and Unwin.

4. Chiang. C.L. (1968): Introduction to Stochastic Process in Biostatistics, John Wiley.

5. Cox, P.R. (1970): Demography, Cambridge University Press.

6. Keyfitz, N. ( 1977): Applied Mathematical Demography, Springer Verlag.

7. Spiegelman, M. (1969): Introduction to Demography Analysis Harvard University . 8. Wolfendon, H.H. (1954): Population statistics and their Compilation, America! Actuarial

Society.

9. Ramkumar R Technical Demography.

10. Coale A.J. (1972): The growth and structure of human population.

11. Keyfitz, N. (1971): An introduction to mathematics of population.

12. Bogue, D.J.: Principles of Demography.

Appendix:B

BOS: 03-04-2018



M.A./M.Sc. IV Semester(Statistics)

Course Code-STM4004

Operations Research


Course Objectives: To introduce the basic and advanced concepts of Operations Research


Describe the technique of Operations Research

Apply the theory of inventory and project scheduling in real life application

Syllabus

Unit I: Linear Programs, Review of Simplex Method, Revised Simplex Method, Sensitivity

Analysis, Parametric Programming and Integer Programming: Applications of Integer

programming, Branch and Bound and Gomory's Cutting Plane Methods.

Unit II: Dual linear programs: Primal-Dual Relationship, Shadow Prices, Dual Simplex Method

and Column Dual Simplex Method, Duality theorems: Weak Duality, Strong Duality,

Complementary Slackness Theorem and Complementary Slackness Conditions with applications.

Unit III: Deterministic Inventory Systems: The components of an inventory system, Demand and

replenishment pattern. The Problem of EOQ with uniform demand and several production runs of

unequal length. The problem of EOQ with finite rate of replenishment. The problem of EOQ with

shortages.

Unit IV: Project scheduling: Network representation of a Project Rules for construction of a

Network. Use of Dummy activity. The critical Path method (CPM) for constructing the time

schedule for the project. Float (or shack) of an activity and event. Programme Evolution and

Review Technique (PERT). Probability considerations in PERT. Probability of meeting the

scheduled time. PERT Calculation, Distinctions between CPM and PERT.

Books Recommended:

1. Gass, S.I.: Linear Programming-Methods & Applications. Boyd & Fraser Publishing

Company, Danvers, Massachusetts, 5th edition, 1985.

2. A.Ravindaran, Don T. Philips and J.J.Soleberg : Operations Research: Principles and

Practice, 2nd ed., Wiley india-2007

3. Hillier & Liberman: Introduction to Operations Research, Mc. Graw Hill Book Co.

4. Taha, H.A.: Operations Research-An introduction, Prentice Hall of India Pvt. Ltd.

New Delhi. (11th Edition-2003)

5. Swaroop K, Gupta, P.K. & Mohan, M.: Operations Research, Sultan Chand & Sons,

New Delhi.2007

6. Salkin, H.M.: Integer Programming, Addison Wesley, 1975.

Appendix B

BOS 30.07.2016



M.A./M.Sc.(Operations Research)

IV Semester

Course Code-STM/ORM4005

Queuing Theory & Applied Stochastic Processes


Course objectives: To introduce the elementary and advanced concepts of queuing theory.


Describe the applied concepts of stochastic process.

Apply the tools of stochastic process in queuing models and other related areas of

applications.

Syllabus

Unit I: Concepts of Death and Birth process in Queuing system, Elements of Queuing System,

steady state solution, Measures of effectiveness of (M/M/1): )/( FIFO , (M/M/1): )/( NFIFO ,

(M/M/S): )/( FIFO , (M/M/S): )/( NFIFO ,Waiting time distribution of M/M/1 and M/M/S

models.

Unit II: Non Markovian Queuing Systems: Concept of embedded Markov chain, Steady state

solution, Mean number of arrivals, expected queue length and expected waiting time in

equilibrium. )1//( KEM Model - Concept of Erlangian service distribution, steady state solution,

Measures of effectiveness. Introduction to Queuing Systems Networks.

Unit III: Machine Repair Models - (M/M/1): (GD/M/n), (M/M/c): (GD/M/n). Power Supply

Models, Deterministic Models. Application of Stochastic Process on System Reliability:

Availability and maintainability concepts, Markovian models for reliability and availability of

repairable two-unit systems, Replacement model, Maintained system, Minimal Repair Replacement

Polices.

Unit IV: Stochastic Processes on survival and competing risk theory: Measurement of competing

risks, inter-relations of the probabilities, estimation of crude, net & partially crude probabilities,

Neyman’s modified Chi-square method, Independent & dependent risks.

Books Recommended:

1. Mehdi, J. (1994): Stochastic Processes, Wiley Eastern, 2nd Ed.

2. Sheldon, M. Ross (1996): Stochastic Processes, Wiley Eastern, 2nd Ed.

3. Groos, Da Harris, C.M. (1985): Fundamental of Queuing Theory, Wiley.

4. Biswas, S. (1995): Applied Stochastic Processes, Wiley.



M.A./M.Sc.(Statistics)

IV-Semester

Course Code-STM4071

Lab. Course – Based on STM-4001, 4002, 4003


Appendix A

BOS 20.10.2016



M.A./M.Sc.

Course Code-STM4091

Applied Statistics

An open elective course to be offered to M.A./M.Sc. Students of Faculty of Science other than

M.A./M.Sc. (Statistics) and M.A./M.Sc. (Operations Research)

Credits 04 M.M.: 30+70=100

Course objectives: To introduce the elements of applied statistics


Describe the concepts of applied statistics in real life scenario.

Apply the techniques in data science.

Syllabus Unit I: Measures of central tendency, measures of dispersion, measures of skewness and kurtosis,

basic concept of probability theory, introduction to random variables and its probability

distributions, standard probability distributions: Bernoulli, binomial, Poisson, geometric, normal,

exponential and lognormal.

Unit II: Bivariate data and scatter diagram, simple correlation, partial and multiple correlation,

simple and multiple regression analysis, sampling distributions, testing of hypothesis, p-value, Z-

test, t-test, F-test and Chi-square test.

Unit III:Principles of experimental design, statistical models for experimental design, completely

randomized design, randomized block design, Latin square design, analysis of variance for one-

way and two-way classifications.

Unit IV: Concept of sample surveys, simple random sampling with replacement and without

replacement, stratified random sampling, systematic random sampling, ratio and regression

methods.

Books Recommended

1. Andrew F. Siegel (1988): Statistics and Data Analysis: An Introduction’ John Wiley &

Sons, Inc. New York

2. John E. Freund (1979):Modern Elementary Statistics, Fifth Edition, Prentic-Hall, Inc.,

Englewood Cliffs, New Jersey.

3. Snedecor, G. W. and Cochran, W. G. (1989): Statistical Methods, 8th

Ed., Wiley India.

4. R. Lyman Ott and Michael Longnecker (2001): An introduction to Statistical Methods and

data analysis, 5th

Ed., Thomson Learning, Inc.

5. Hogg R.V., Tanis E.A. & Zimmerman, D. (2014): Probability and Statistical Inference, 9th

Ed., Pearson Education.

6. Montgomery, D. C. (2013): Design and analysis of experiments, 8th

Ed., John Wiley &

Sons, Inc.

7. Cochran, W.C. (1977): Sampling Technique, 3rd

Ed., John Wiley & Sons, Inc.

Last updated 27.12.2019