## UG 120 1 Syllabus Mumbai University by munotes

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UNIVERSITY OF MUMBAI

Syllabus for the M. A./ M. Sc. PART II

(Semester III and Semester IV)

Program: M. Sc.

Course : STATISTICS

(Choice Based Credit System with effect from the

academic year 201 9–2020)

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M.A./ M.Sc. Part - II

(Semester III and Semester IV) Syllabus

Revised for choice based and credit system

To be impleme nted from the Academic year 2019 -2020

Structure of the syllabus:

In both, semester III and semester IV, there are three compulsory courses each of four credits and

one course of four credit s can be selected from the available list of elective courses. In addition

there are two practical courses each of four credits in semester I II and one practical course of four

credits and Statistical project of four credits in semester IV.

Following is the t able showing the proposed courses (compulsory and elective) to be covered in

semester III and semester IV of second year .

COURSE PSST 30 1 PSST 30 2 PSST 30 3 PSST 30 4 PSST P3A &

PSST P3B

SEMESTER

III MULTIVARIATE

ANALYSIS - II TESTING OF

HYPOTHES ES PLANNING AND

ANALYSIS OF

EXPERIMENTS -

II

ELECTIVE

COURSE STATISTICS

PRACTICAL -

V

STATISTICS

PRACTICAL -

VI

COURSE PSST 401 PSST 402 PSST 403 PSST 404 PSST P4A &

PSST P4B

SEMESTER

IV STOCHASTIC

PROCESSES TIME SERIES

ANALYSIS RELIABILITY

AND SURVIVAL

ANALYSIS

ELECTIVE

COURSE STATISTICS

PRACTICAL -

VII

STATISTICAL

PROJECT

Duration of each of the theory course s, will be 120 hou rs which is further divided into two parts

Total number of classroom teaching hours 60

Total number of notional hours 60

Each theory course will be of four credits having four hours of classroom teaching per week .

Syllabus of each theory course is d ivided into four units each should be covered in 15 lectures

each of one hour.

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4 SEMESTER III

COMPULSORY COURSES

DETAILED SYLLABUS:

Unit Course Code: PSST 301

Course Title: MULTIVARIATE ANALYSI S - II

I Principal Component Analysis : population and sample principal components, principal

components for special structure of dispersion matrix: diagonal matrix , correlation matrix,

sample variation, interpretation of sample principal components, graphing the principal

components, large sample inferen ce, large sample confidence interval for eigenvalues ,

test for equal correlation structure.

II Factor Analysis : introduction, methods of estimation: principal components method,

maximum likelihood method. Factor rotation , factor scores .

III Canonical Co rrelation and Variates: introduction, interpretation, sample canonical

correlation and covariates, large sample inference.

IV Cluster Analysis : similarity measures, hierarchical clustering methods and non -

hierarchical methods. Multidimensional scaling.

REFERENCE BOOKS :

Anderson, T. W. (2003): An Introduction to Multivariate Statistical Analysis. John Wiley.

3rd edition.

Giri, N. C. (2003): Multivariate Statistical Analysis. CRC Press. 2nd edition.

Hardle, W. K. and Hlavka, Z. (2015): Multivariate St atistics: Exercise and solutions.

Springer.

Johnson , R. A. and Wichern , D. W. ( 2015): Applied Multivariate Statistical Analysis . 6th

Edition . PHI Learning Private Limited.

Kshirsagar , A. M. (1979) : Multivariate Analysis, Marcel Dekker Inc. New York.

Mukhop adhyay , P. (2008) : Multivariate Statistical Analysis. World Scientific.

Srivastava , M. S. (2002) : Methods of Multivariate Statistics . John Wiley.

Unit Course Code: PSST 302

Course Title: TESTING OF HYPOTHESES

I Fundamental notions of testing of hy pothesis: Statistical hypothesis, simple and

composite hypothesis, critical region, acceptance region, type I and type II error s, test

function, test of hypothesis, power of test , power function .

Best critical region, most powerful test, Neymann -Pearson le mma.

uniformly most powerful (UMP) test, monotone likelihood ratio property of family of

distributions , non existence of UMP .

II Generalized Neyma nn-Pearson Lemma, Locally Most Powerful test (LMPT). UMP

Unbiased test, Locally Most Powerful Unbiased test. Likelihood ratio test.

Confidence sets: Uniformly Most Accurate (UMA), Uniformly Most Accurate Unbiased

(UMAU) confidence sets. Sequential Probability Ratio Test (SPRT).

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5 III Definitions: Quantile, Quantile function, Empirical distribution function, Empirical

quantile function. Point estimation and interval estimation of population quantiles. Test of

hypotheses for population quantile.

U-statistics : definition, properties, one sample and two sample theorem.

One and two samples problem s, Sign test a nd Wilcoxon’s test, Wald Wolfowitz run test,

Mann -Whitney U -test, Wilcoxon Rank -Sum test. Test for equality of k independent

samples: Median test , Kruskal Wallis test, Friedman test.

IV Goodness of fit tests: Chi -square goodness of fit test, Kolmogorov -Smirnov test – one and

two sample tests . Measures of association and their tests of significance: Kendall’s Tau

coefficient, Spearman’s coefficient of rank correlation.

REFERENCE BOOKS:

Dixit , U. J. (2016): Examples in Parametric Inference with R, Spri nger.

Gibbons , J. D. and Chakrab orti, S. (2010) : Nonparametric Statistical Inference . CRC Press.

5th Edition.

Lehmann, E. L. and Romano, J. P. (2005): Testing Statistical Hypothesis, Springer . 3rd

Edition .

Randles, R. H. and Wolfe, D. A. (1979): Introduct ion to the theory of nonparametric

statistics. John Wiley.

Rohtagi, V. K. and A.K.M.AD. Ehsanes Saleh (2001) : An Introduction to Probability and

Statistics. John Wiley . 2nd Edition.

Shao , J. (2005): Mathematical Statistics. Springer. 2nd Edition.

Srivast ava, M. K. and Srivastava, M. (2014) Statistical Inference: Testing of Hypotheses.

PHI Learning private limited.

Wald , A. (1947) : Sequential Analysis.

Unit Course Code: PSST 303

Course Title: PLANNING AND ANALYSIS OF EXPERIMENTS - II

I Partially bal anced incomplete block design, Lattice design. Row Column Design, La tin

Square design, Youden Square Design

II Split Plot Design, Weighing designs, Hadamard Matrix and its relation to the weighing

design, optimality of above design: A,D,E

III 3k factoria l design, confounding in 3k factorial design, 3k fractional factorial design.

Factorial design s with mixed levels.

IV Response surface methodology, the method of steepest ascent, analysis of second order

response surface, experimental designs for fitting response surfaces. Evolutionary

operations . Robust designs .

REFERENCE BOOKS :

Chakrabarti, M. C. (1962): Mathematics of Design and Analysis of Experiments. Asia

Publishing house.

Das, M. N. and Giri, N. C. (2002): Design and Analysis of Experiments. Ne w Age

International. 2nd Edition.

Dean, A., Voss, D, and Draguljic, D. (2017): Design and Analysis of Experiments.

Springer. 2nd Edition.

Kempthorne, O. and Hinkelman, K. (2008): - Design and analysis of experiments:

Introduction to experimental design. V olume I. John Wiley. 2nd Edition.

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6 Kempthorne, O. and Hinkelman, K. (2005): - Design and analysis of experiments:

Advanced experimental design. Volume II. John Wiley. 2nd Edition.

Khuri, A. and Cornell, J. A. (1996): Response surfaces: Design and analyses. Marcel

Dekker. 2nd Edition.

Meyers, R. H., Montgomery, D. C. and Christine, M. (2016) : Response surface

methodology: Process and Product Optimization using designed experiments. John Wiley.

4th Edition.

Montgomery , D. C. (2017) : Design and Analysis o f Experiment s. John Wiley. 9th Edition.

Raghavarao , D (1988) : Construction and Combinatorial Problems in Design of

Experiments . Dover Pubns.

Wu, C. F. Jeff and Hamada, M. (2002) : Experiments: planning, analysis, and parameter

design optimization , John Wiley.

Shah , K. R. and Sinha , B. K. (1989) : Theory of Optimal Designs. Springer.

ELECTIVE COURSES:

In Semester three, any one elective course is to be selected from the following five elective

courses.

1. PSSTE 1 304: FINANCIAL MATHEMATICS .

2. PSSTE 2 304: ELEMENTS OF DATA SCIENCE.

3. PSSTE 3 304: STATISTICAL PROCESS CONTROL .

4. PSSTE 4 304: CATEGORICAL DATA ANALYSIS .

5. PSSTE 5 304: MEASURE THEORY.

DETAILED SYLLABUS:

Unit Course Code: PSST E1 304

Course Title: FINANCIAL MATHEMATICS

I Interest rates, Binomial trees

II Wiener processes and Ito's lemma, The Black -Scholes -Merton model

III Value at Risk.

IV Estimating volatilities and correlations.

REFERENCE BOOKS:

Hull, J. C. (2006): Options, Futures and Other Derivatives, 6th Edition.

Ross, S. M. (2011): An El ementary Introduction to Mathematical Finance. Cambridge

University Press. 3rd Edition.

Ruppert, D. (2004): Statistics and Finance: An Introduction. Springer.

Unit Course Code: PSST E2 304

Course Title: ELEMENTS OF DATA SCIENCE.

I Introduct ion to Data Mining , Classification techniques, CART, Random forests, Bayesian

classification and learning rules. Introduction to Big Data. Large dimension small size

multivariate data analysis , tackling the problems of estimation and inference.

Classificat ion of Big Data , Screening and Variable Selection.

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7 II Dimension Reduction and Visualization Techniques, Algorithms for data -mining using

multiple nonlinear and nonparametric regression , Lasso Regression , Projection Methods,

penalty, ridge regression, Boo tstrap methods.

III Introduction to Nonlinear regression, introduction to Nonparametric regression,

generalized additive models, kernel methods, neural network, Artificial Intelligence,

machine learning. Introduction to Structured Data and Structural Eq uation Modeling.

IV Neural Networks: Multi -layer perceptron, predictive ANN model building using back

propagation algorithm , Exploratory data analysis using Neural Networks – self organizing

maps. Genetic Algorithms, Neuro -genetic model building.

REFERE NCE BOOKS:

Breiman, L., Friedman, J. H., Olschen, R. A. and Stone, C.J. (1984): Classification of

Regression Trees, Wadsowrth Publisher.

Hand, D. J. , Mannila, H. and Smith, P. (2001): Principles of Data Min ing, MIT Press,

Cambridge.

Hassoun, M. H. (199 8): Fundamentals of Artificial Neural Networks, Prentice -Hall of

India, New Delhi.

Hardle, W.(1990): Applied Nonparametric Regression, Cambridge University Press.

Hastie, T. and Tibshirani, R.(1990): Generalized Additive Models, Chapman and Hall,

London.

Hastie, T., Tibshirani, R. and Friedman, J. H. (2001): The elements of Statistical Learning:

Data Mining, Inference & Prediction, Springer Series in Statistics, Springer - Verlag.

Hastie, T., Tibshirani, R. and Wainwright, M. (2015): Statistical Learning wi th Sparsity:

The Lasso and generalizations.

Seber, G. A. F. and Wild, C. J. (1989): Nonlinear Regression, John Wiley.

Unit Course Code: PSST E3 304

Course Title: STATISTICAL PROCESS CONTROL

I Process and Measurement System Capability Analysis. Cu mulative sum and

Exponentially Weighted Moving Average Control Charts.

II Modified and Acceptance control charts. Group control charts for multiple -stream

processes. Multivariate quality Control. SPC with correlated data.

III Engineering Process Control , Process Design and Improvement with Designed

Experiments , Process Optimization with Designed Experiments , Robust Deign and Signal

to Noise Ratios .

IV Introduction to Lean and six – sigma: Definition of Lean, 5 S in Lean, 7 wastes in lean, 5

principles o f lean. Definition of six – sigma and definition of Lean six – sigma.

DMAIC over view, Define phase : VOC,VOB,VOP,CTQ,COPQ ,Project

charter, DPU, DPMO, Yield, Brain Storming, SIPOC, Cause and Effect diagram

Measure phase: Process definition, Process Ma pping, Value Stream Mapping, sigma

calculation using sigma calculator, Gage R and R.

Improve Phase: Multi voting, Delphi Technique, Nominal group technique, Kaizen.

ISO 9000.

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8 REFERENCE BOOKS :

1. Duncan, A. J. (1986): Quality Control and Industrial S tatistics. Irwin. 5th Edition.

2. Grant, E. L. and Leavenworth, R. (2017): Statistical Quality Control. McGraw Hill. 7th

Edition.

3. Johnson, N. L. (1977): Statistics and Experimental Design in Engineering and Physical

Science. John Wiley.

4. Montgomery , D. C. (2004): Introduction to Statistical Quality Control . John Wiley. 4th

Edition .

5. Muralidharan, K. (2015): Six sigma for organizational Excellence: A statistical approach.

Springer.

6. Phadke , M. S. (1989): Quality Engineering Using Robust Design . Pearson.

7. Taguchi, G. (1986) : Intr oduction to Quality Engineering: Designing quality into products

and processes. Quality resources.

Unit Course Code: PSST E4 304

Course Title: CATEGORICAL DATA ANALYSIS

I Models for binary response variables, log l inear models, fitting log linear and logit

models.

II Building and applying l og linear models, log linear -logit models for ordinal variables.

III Multinomial response models, models for matched pairs.

IV Analyzing repeated categorical response data, asymptotic theo ry for parametric models,

estimation theory for parametric models

REFERENCE BOOKS :

Agresti , A. (2012 ): Categorical Data Analysis. John Wiley. 3rd Edition.

Cox, D. R. and Snell, E. J. (1989): The Analysis of Binary Data. CRC Press. 2nd Edition.

Gokhal e, D. V. and Kullback , S. (1978): The Information in Contingency Tables. Marcel

Dekker.

Hosmer, D. W. and Lemeshow, S. (2000): Applied Logistic Regression. John Wiley, 2nd

Edition.

Unit Course Code: PSST E5 304

Course Title: MEASURE THEORY

I Introduction to sets and classes, f ield, sigma field, Borel field. Measure Spaces: Measures,

measures on intervals, properties of measures, outer measure, measureable sets, extension

of measures, Lebesgue measure, non measurable sets, Measurable functions, con vergence

of measures , introduction to L p spaces.

II Integration: i ntegra l of measurable function, integrable functions, Fatou’s lemma,

monotone convergence theorem, dominated convergence theorem, Radon -Nikodym

theorem, Hahn and Jordan decomposition theor em,

III Product spaces, product measures, Fubini’s theorem, convergence in measure, probability

spaces.

IV Conditional probability, conditional expectations, independence, Marting ale theory ,

marting ale convergence theorem, marting ale central limit theor em.

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REFERENCE BOOKS:

Athreya, K. B. and Lahiri S. (2006). Measure Theory and Probability Theory , Springer.

Billingsley, P. (1995). Probability and Measure , 3rd Edition, John Wiley .

Chandra, T. and Gangopadhyay, S. (2017): Fundamentals of Probability Th eory. Narosa

Publishing House.

Chung, K. L. (2001). A Course in Probability Theory , Third Edition, Academic Press.

Doob, J. L. (1994): Measure Theory. Spring -Verlag.

Halmos, P. R. (1950): Measure Theory. Spring -Verlag.

Loeve, M. (1963): Probability theory. D. Van Nostrand compny Inc.

PRACTICAL COURSES:

PSST P3A STATISTICS PRACTICAL -V

Practical s Based on Multivariate Analysis II (PSST 301) and

Testing of Hypothesis (PSST 302) .

PSST P3B STATISTICS PRACTICAL -VI

Practical s Based on Planning and Analysi s of Experiments -II

(PSST 303) and Elected course (PSST 304).

Each batch of practical consists of 10 students .

Duration of each of the practical course, will be 120 hours which is further divided into two parts

Total number of practical hours 60

Total number of notional hours 60

Each practical course will be of four credits. Each practical will have four hours of practical

session per week per batch of practical.

Contents of the practical courses, PSST P3A and PSST P3 B are to be covered with the help of

Statistical Sof tware s like SAS, SPSS, MINITAB, R-Environment etc.

Seminar : Case Studies listed in the paper to be discussed and brief summary should be prepared.

2 hours per week: (30 teaching hours + 30 notional hours)

= 60 hours

= 2 credits

Total number of credits for third semester:

Theory courses: 16

Practical courses: 08

Total 24

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10 EXAMINATION PATTERN FOR THEORY COURSES

Each course will be evaluated in two parts,

Part A ] Con tinuous Internal Evaluation (C IE) and

Part B] Semester End Examination (SEE)

CIE will be of 40 marks which will include one mid -semester test of 20 marks of one hour

duration and other 20 marks are composed of any one or combinations of group discussion, viva-

voce, open notebook test, surprise test, assignments, class participation etc to be conducted by

respective teacher.

SEE will be a theory exam ination of 60 marks of three hours duration based on entire syllabus.

The question paper will consist of fiv e questions of 15 marks each. Student should answer any

four questions out of five questions.

EXAMINATION PATTERN FOR PRACTICAL COURSES

At the end of semester there will be a practical examination of 100 marks and of three hours

duration for each of th e practical courses, PSST P3A and PSST P3B. The distribution of total of

100 marks is as given below ,

Practical Examination Viva Journal Total

80 marks 10 marks 10 marks 100 marks

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SEMESTER I V

COMPULSORY COURS ES

DETAILED SYLLABUS:

Unit Course Code: PSST 401

Course Title: STOCHASTIC PROCESSES

I Introduction to stochastic processes, specification of stochastic processes, real life

applications of stochastic processes, introduction to different types of stoch astic

processes.

Markov chain, real life examples of Markov chain, order of a Markov chain , transition

probabilities, Chapman -Kolmogorov equations, classification of states, periodicity, closed

class, minimal closed class, stationary distribution of a Mar kov chain. Gamblers ruin

problem, random walk. Conc ept of absorption probabilities, Statistical inference for

Markov chains.

II Continuous time Processes: Poisson process, Generalizations of Poisson process, birth

and Death process.

Brownian Motion, Wien er process, Kolmogorov equations.

III Renewal Process: Renewal process in continuous time, renewal equation, stopping time,

renewal theorem. Real life applications.

III Branching Process: Introduction to branching process, probability generating functio n of

branching process, moments, classification of states, identification of criticality

parameter, extinction probability, relationship between criticality parameter and

extinction probability of the process, Expression for mean and variance of the proces s.

Extinction probability, Some applications.

REFERENCE BOOKS :

Bhat , B.R. (2000). Stochastic Models: Analysis and Applications , New Age International.

Bhat, U. N. and Miller , G. K. (2002): Elements of Applied Stochastic Processes. 3rd

Edition. Wiley

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12 Basu, S (2012): Applied Stochastic Processes. New Central book agency.

Durrett , R. (1999): Essentials of Stochastic Process.

Hoel, P. G., Port, S. C. and Stone, C. J. (1972) : Introduction to Stochastic Processes , Houghton

Mifflin

Karlin , S. and Taylor , H. M. (1975): First Course in Stochastic Processes second edition.

Kulkarni, V. G. (2011): Modeling and Analysis of Stochastic Systems, Chapman and Hall,

London.

Medhi , J. (1994): Stochastic Processes Second edition, Wiley Eastern.

Ross , S. M. (2004): Introduct ion to Probability Models, Wiley Eastern.

Unit Course Code: PSST 402

Course Title: TIME SERIES ANALYSIS

I Real life examples of time series, types of variation in time series, exploratory time series

analysis, tests of randomness, tests for trend, sea sonality. Auto -covariance and auto -

correlation functions and their properties, Exponential and Moving average smoothing.

Holt -Winters smoothing. Forecasting based on smoothing, adaptive smoothing. Time -

series as a discrete parameter stochastic process. Portmanteau tests for noise sequences,

transformation to obtain Gaussian series. General linear processes.

II Auto regressive (AR), Moving average (MA) and Autoregressive moving average

(ARMA), Stationarity and invertibility conditions. Nonstationary and seasonal time series

models: Auto regressive integrated moving average (ARIMA) models, Seasonal ARIMA

(SARIMA) models, Transfer function models (Time series regression).

III Estimation of mean, auto covariance and autocorrelation functions, Yule -Walker

estimation. Forecasting in time series models, Durbin -Levinson algorithm, innovation

algorithm.

IV Estimation of ARIMA model parameters, Choice of AR and MA periods, FPE, AIC, BIC,

residual analysis and diagnostic checking, Unit -root nonstationarity, unit -root tests,

ARCH and GARCH models.

REFERENCE BOOKS :

Brockwell, P. J. and Davis, R. A. (2003): Introduction to Time Series Analysis, Springer

Chatfield, C. (2001): Time Series Forecasting, Chapman &Hall.

Fuller, W. A. (1996): Introduction to Statistica l Time Series, 2nd Ed. Wiley.

Hamilton, N. Y. (1994): Time Series Analysis, Princeton University press.

Kendall, M. and Ord, J. K. (1990): Time Series, 3rd Ed. Edward Arnold.

Lutkepohl, H. (2005): New Introduction to Multiple Time Series Analysis, Sprin ger

Shumway, R. H. and Stoffer, D. S. (2010): Time Series Analysis & Its Applications,

Springer.

Tsay, R. S. (2010): Analysis of Financial Time Series, Wiley.

Unit Course Code: PSST 403

Course Title: RELIABILITY AND SURVIVAL ANALYSIS

I Survival fun ction, Hazard function, cumulative hazard function, reversed hazard function,

nature of hazard function, bath -tub shape hazard function, class of increasing failure rate

distributions, decreasing failure rate distributions, theorems. Relations between surv ival

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13 function, probability function, hazard function, cumulative hazard function, reversed

hazard function.

Lifetime distributions: exponential, Weibull, gamma, extreme value distributions, log -

normal etc.

II Reliability of the system: structure function , standard systems: series system, parallel

system, k -out-of-n system, coherent system, path sets and path vectors, minimal path sets,

cut sets and cut vector, minimal cut sets, reliability of coherent system, reliability bounds.

III Introduction to Survi val Analysis: need of survival analysis, censoring: left censoring,

right censoring, interval censoring, random censoring, times censoring, order censoring,

hybrid censoring.

Kaplan -Meier estimator of survival function, properties of Kaplan -Meier estimator ,

Nelson -Aalen estimator of cumulative hazards function.

Linear and log -transformed confidence interval for survival function and cumulative

hazard function.

Q-Q plot, hazards plot for lifetime distributions.

Competing risk models.

IV Regression models in Survival analysis: proportional hazards model, Accelerated failure

time model, Cox proportional hazards model, residual analysis of proportional hazards

model.

Frailty models: Univariate frailty, multivariate frailty models, shared frailty, correlated

frailty, additive frailty models. Using Weibull as baseline and gamma as frailty

distribution.

REFERENCE BOOKS :

Barlow , R. E. and Proschan , F. (1965): Mathematical theory of reliability

Barlow , R. E. and Proschan , F. (1975): Statistical theory of reliabil ity and life testing. Holt,

Reinhart and Winston.

Deshpande , J. V. and Purohit, S. G. (2 005). Life Time Data: Statistical Models and

Methods , Wor ld Scientific.

Hanagal, D. D. (2011). Modeling Survival Data Using Frailty Models. CRC Press.

Hosmer, D. and Lemeshow, S. (1999). Applied Survival Analysis: Regression Modeling of

Time to Event Data , Wiley, New York.

Kalbfleisch, J. D. and Prentice, R.L. (1986): The Statistical Analysis of Failure Time Data,

John Wiley.

Kleinbaum , D. G. and Klein , M. (2012). Survival Analysis : A Self -Learning Text , 3rd Ed,

Springer, New York.

Lawless, J.F.(1982): Statistical models and methods for life time data. John Wil ey.

Lee, E. T. and Wang, J. W. (2003). Statistical Methods for Survival Data Analysis ,

3rd Edition. John Wiley.

Liu, X. (2012). Survival Analysis: Models and Applications , Wiley, New York.

Ross S. M. (2014): Introduction to Probability Models. Elsevier. 11th Edition.

Smith, P.J. (2002): Analysis of Failure and Survival data. CRC.

Wienke, A. (2011). Frailty Models in Survival Analysis, CRC.

ELECTIVE COURSES:

In Semester four, any one elective course is to be selected from the following five elective

courses.

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14 1. PSSTE 1 404: ADVANCE D THEORY OF DESIGNS.

2. PSSTE2 404: OPERATIONS RESEARCH.

3. PSSTE3 404: STATISTICAL DECISION THEORY

4. PSSTE 4 404: STATISTICS IN INSURANCE.

5. PSSTE 5 404: MODERN STATISTICAL INFERENCE.

DETAILED SYLLABUS:

Unit Course Code: PSST E1 404

Course Title: ADVANCE D THEORY OF DESIGNS

I Optimality of block designs, optimality of weighing designs

II Two-level fractional factorial designs, process improvement with steepest ascent

analysis of response surfaces.

III Experimental designs for fitting response surfaces, response surface methods and

Taguchi’s robust parameter designs.

IV Experiments with mixtures, analysis of mixture data.

REFERENCE BOOKS :

Chakrabarti, M. C. (1962): Mathematics of Design and Analysis of Experiments. Asia

Publishing house.

Cornell, J. A. (2002): Experiments with Mixtures: Designs, Models and the Analysis of

Mixture Data. John Wiley. 3rd Edition.

Das, M. N. and Giri, N. C. (2002): Design and Analysis of Experiments. New Age

International. 2nd Edition.

Dean, A., Voss, D, and Draguljic, D. (2017): Design and Analysis of Experiments.

Springer. 2nd Edition.

Hinkelman, K. (20 12): Design and analysis of experiments: Special Designs and

Applications. Volume III. John Wiley.

Kempthorne, O. and Hinkelman, K. (2008): Design and analysis of experiments:

Introduction to experimental design. Volume I. John Wiley. 2nd Edition.

Kempthorne, O. and Hinkelman, K. (2005): Design and analysis of experiments: Advanced

experimental design. Volume II. John Wiley. 2nd Edition. =

Khuri, A. and Cornell, J. A. (1996): Response surfaces: Design and analyses. Marcel

Dekker. 2nd Edition.

Meyers, R. H., Montgomery, D. C. and Christine, M. (2016) : Response surface

methodology: Process and Product Optimization using designed experiments. John Wiley.

4th Edition.

Montgomery , D. C. (2017) : Design and Analysis of Experiment s. John Wiley. 9th Edition.

Raghavarao, D (1988): Construction and Combinatorial Problems in Design of

Experiments. Dover Pubns.

Wu, C. F. Jeff and Hamada, M. (2002) : Experiments: planning, analysis, and parameter

design optimization, John Wiley.

Shah, K. R. and Sinha, B. K. (1989): Theory of Optimal Designs. Springer.

Cours e

Code UNIT

OPERATIONS RESEARCH

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15 PSST

404 I Linear programming problem: Review of Line ar programming problem, convex

set, Hyperplane, simples method, Revised simplex method, Dual simplex

method.

II Integer Linear programming: Gomory cut method, branch and bound method,

fractional cut method.

Non-Linear programming: Kuhn -Tucker conditio ns of optimality. Quadratic

programming; methods due to Beale, Wofle and Vandepanne, Duality in

quadratic programming.

III Inventory Management: Introduction to Inventory control problem, Type of

Inventory, Different cost in Inventory Problem, Selectiv e control techniques

Techniques of Inventory models : EOQ with known demand , uniform demand,

problem of EOQ with shortages, Inventory model with stochastic demand ,

Buffer stock, price discounts.

back order inventory models.

IV Queuing theory: Introd uction of Queuing theory, Elements of a Queuing model,

Pure birth and death model, specialized poison queues,

single server models: (M/M/1):(GD/

/ ), M/M/1:( GD/M/

) , Multiserver

models

Data Envelopment Analysis (DEA) : meaning and use of DEA.

REFERENCE BOOKS :

Hadley, G. ( 2002 ): Linear Programming . Narosa.

Kambo, N. S. (2008): Mathematical Programming Techniques. Affiliated EastWest Press

Pvt.

Taha, H. A. (2010 ): Operations Research: An introduction. Pearson . 9th Edition.

Winston , W. L. (2003): Operations Research : Applications and Algorithms . Cengage

Learning. 4th Edition.

Shanti swarup: Operations Research

Software :

1. Microsoft solver for topics 1 to 7

2. LINDO (Linear Interactive and Discrete Optimizer), LINGO for topics 1 to 7

3. Microsoft project for PERT and CPM

4. Crystal Ball for simulation

Unit Course Code: PSSTE3 404

Course Title: STATISTICAL DECISION THEORY

I Formulation of decision problems, randomized and nonrandomized decision rules,

illustrative exa mples, loss function, risk function , prior distributions, conjugate priors,

posterior distributions .

II Optimum decision rules, Bayes’ rule, minimax rule, admissibility of rules, sufficiency and

Rao-Blackwellization.

III Bayes’ test procedures, Bayesi an estimation, credible sets, Bayesian hypothesis testing,

Bayesian prediction .

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16 IV Empirical Bayes’ analysis, Bayesian computations , Bayesian comparison.

REFERENCE BOOKS :

Berjer, J. O. (1985): Statistical Decision Theory and Bayesian Analysis. Springe r.

Box, G. E. P. and Tiao, G. C. (1992): Bayesian Inference in Statistical analysis. John

Wiley.

DeGroot , M. H. (2004 ): Optimal Statistical Decision. John Wiley.

Ferguson, T. S. (1967): Mathematical Statistics: A decision theoretic approach. Academic

Press.

Ghosh , B. K. (1970) : Sequential Tests of Statistical Hypothesis . Addison -Wesley

Publication.

Savage, L. J. (1972 ): The f oundations of Statistics. Dover Publications.

Unit Course Code: PSST E4 404

Course Title: STATISTICS IN INSURANCE

I Principle s of Insurance . Need of Insurance . (Utility Theory). Difference between Banks

and Insurance Companies . Brief history of Insurance .

II Types of Insurance & Insurance products

a. Life insurance - Term Assurance, Endowment Assurance, Annuities etc.

b. Non -life insurance

c. Health insurance

Role of an Actuary . Actuarial Principles of Life and Health insurance including time

value of money .

III Gross Premium and Net Premium calculation . Life Insurance Reserves. Risk Premium

calculation. Statisti cal distributions useful in General Insurance .

IV Credibility Theory and Bayes' Theorem . Pension plans and Wealth Management .

Risks - Types of Risk and Risk Management including Underwriting.

REFERENCE BOOKS :

Black, K. and Skipper, H. D. (2015): Lif e insurance. Lucretian

Bowers , N. L.. Gerber, H. U., Hickman, J. C., Jones, D. A. and Nesbitt, C. J. (1997) :

Actu arial Mathematics. Society of Actu aries of London. 2nd Edition.

Unit Course Code: PSST E5 404

Course Title: MODERN STATISTICAL INFERENCE .

I Bayesian inference: Point estimators, Bayesian HPD confidence intervals, testing,

credible intervals, prediction of a future observation Model selection and hypothesis

testing based on objective probabilities and Bayes’ factors large sample methods: Limit of

posterior distribution, consistency of posterior distribution, asymptotic normality of

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17 posterior distribution.

II EM algorithm: Incomplete data problems, E and M steps, convergence of EM algorithm,

standard errors in the context of EM algorithm, applications of EM algorithm, Bayesian

approach to EM algorithm.

III MCMC methods: Methods of generating random sample, Metropolis -Hastings and Gibbs

Sampling algorithms, convergence, applications, Bayesian approach.

IV Bootstrap methods, estimation of sampling distribution, confidence intervals, failure of

Bootstrap, variance stabilizing transformation, Jackknife and cross -validation,

applications.

REFERENCE BOOKS :

Bolstad , W. M. (2010): Understanding computational Bayesian statistics. John Wiley.

Bolstad, W. M. (2017) : Introduction to Bayesian Statistics. John Wiley. 3rd Edition.

Congdon, P. (2006). Bayesian Statistical Modeling, John Wiley

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap methods and their Applications.

Chapman and Hall.

Efron, B. and Hastie, T. (2016). Computer Age Statistical Inference: Algorithms, Evidence

and Data Science. Cambridge University Press.

Gamerman, D . (1997): Markov chain Monte Carlo: Stochastic simulation for Bayesian

inference. Chapman and Hall.

Gelman, A., Carlin, J . B., Stern, H. S. and Rubin, D. B. (2003): Bayesian Data Analysis,

Chapman and Hall. 2nd Edition.

Gilks, W. R., Richardson, S., and Spiegelhalter, D. (eds.) (1995) Markov Chain Monte

Carlo in Practice. Chapman and Hall.

Kundu, D. and Basu, A. (2009): Sta tistical Computing: Existing Methods and Recent

Developments. Narosa.

McLachlan, G.J. and Krishnan, T. (2008) : The EM Algorithms and Extensions. Wiley.

PRACTICAL COURSES:

PSST P 4A STATISTICS PRACTICAL -VII

Practicals Based on all Four Theory course s

PSST P 4B PROJECT

Statistical project for a group of students.

Each batch of practical consists of 10 students.

Duration of the practical course, will be 120 hours which is further divided into two parts

Total number of practical hours 60

Total number of notional hours 60

Practical course will be of four credits. Each practical will have four hours of practical session per

week per batch of practical.

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18 Contents of the practical course, PSST P 4A are to be covered with the help of Statistical Softwares

like SAS, SPSS, MINITAB, R -Environment etc.

Seminar : Case Studies listed in the paper to be discussed and brief summary should be prepared.

2 hours per week: (30 teaching hours + 30 notional hours)

= 60 hours

= 2 credits

Total number of credits for fourth semester:

Theory courses: 16

Practical courses: 08

Total 24

EXAMINATION PATTERN FOR THEORY COURSES

Each course will be evaluated in two parts,

Part A] Continuous Internal Evaluat ion (CIE) and

Part B] Semester End Examination (SEE)

CIE will be of 40 marks which will include one mid -semester test of 20 marks of one hour

duration and other 20 marks are composed of any one or combinations of group discussion, viva -

voce, open notebook test, surprise test, assignments, class participation etc to be conducted by

respective teacher.

SEE will be a theory examination of 60 marks of three hours duration based on entire syllabus.

The question paper will consist of five questions of 15 marks each. The student should answer any

four questions out of five questions.

EXAMINATION PATTERN FOR PRACTICAL COURSES

At the end of semester four there will be a practical examination of 100 marks and of three hours

duration for the practical cour ses, PSST P 4A. The distribution of total of 100 marks is as given

below ,

Practical Examination Viva Journal Total

80 marks 10 marks 10 marks 100 marks

Course PSST P4B is evaluated based on the project report submitted by the students and

presentation based on the analysis of project as,

Guide’s

assessment External judge’s

Assessment at the time of presentation Viva Total

40 marks 40 marks 20 marks 100 marks

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19

Note: It is resolved that the examination pattern for Theory courses of M.Sc. part I (sem I and

sem II) for continuous internal evaluation (CEE) of 40 marks will be same as M.Sc. part II (sem

III and sem IV) from the academic year 2019 -2020.