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Annexure ‘AAB-CD-01’
Course Title: Advanced Real Analysis
Course Code: STAT 602
Credit Units: 4
Level: PG
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1 Course Objectives:
 To understand various properties and important theorems related to real numbers with
their proofs.
 To develop fundamental knowledge and understanding of the many techniques in Real
Variable , such as - differentiation and integration under the sign of integration, question
of convergence of series, Dirichlet’s integral, Laplace and Laplace Steiltjes transform,
which are also employed in the theory of probability distributions. Similarly, BolzanoWeirstrass, Heine Borel theorems etc. are very much useful in Statistical Inference.
2 Prerequisites:
Graduate level knowledge of Mathematics and Statistics
3 Student Learning Outcomes:

The students will be able to apply various techniques of analyzing Real-valued
Variables in further studies of statistical research investigations.
Course Contents/Syllabus
4 Module I:
25
Monotone functions and functions of bounded variation. Real valued functions,
continuous functions, Absolute continuity of functions, standard properties, uniform
continuity, sequence of functions, uniform convergence, power series and radius of
convergence.
5 Module II:
25
Riemann-Stieltjes integration, standard properties, multiple integrals and their
evaluation by repeated integration, change of variable in multiple integration.
Uniform convergence in improper integrals, differentiation under the sign of
integral, Integration under the sign of differentiation. Dirichlet integral.
6 Module III:
25
Introduction to n-dimensional Euclidean space, open and closed intervals
(rectangles), compact sets, Bolzano-Weierstrass theorem, Heine-Borel theorem.
Maxima-minima of functions of several variables, constrained maxima-minima of
functions.
7 Module IV: Applications of mgf and cf for continuous distributions
25
Laplace and Laplace-Steiltjes transforms. Solutitions of linear differential.Properties
TOTAL
CREDIT
UNITS
4
of Laplace transforms, Transforms of derivatives, Transforms of integrals,
Evalualtion of integrals using Laplace transform, convolution theorem.
8 Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a
separate Lab sessions. In addition to numerical applications, the real life problems
and situations will be assigned to the students and they are encouraged to get a
feasible solution that could deliver meaningful and acceptable solutions by the end
users. The focus will be given to incorporate probability and related measures to
develop a risk model for various applications.
9 Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop
down)
Weightage
(%)
70%
End Term
Examination
MidHome
Class
Attendance
Term Assignment Performance/
Exam
Viva
10%
8%
7%
5%
70%
Text & References:






Rudin, Walter (1976). Principles of Mathematical Analysis, McGraw Hill.
Apostol, T. M. (1985). Mathematical Analysis, Narosa, Indian Ed.
Narayan, S., (2010). Elements of Real Analysis, S. Chand and Sons.
Miller, K. S. (1957). Advanced Real Calculus, Harper, New York
Courant, R. and John, F. (1965). Introduction to Calculus and Analysis, Wiley
Bartle, R.G. (1976): Elements of Real Analysis, John Wiley & Sons.
Annexure ‘AAB-CD-01’
Course Title: PROBABILITY THEORY
Course Code: STAT 605
Credit Units: 4
Level: PG
#
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Course Title
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Weightage (%)
1
Course Objectives:
Probability theory and its models serve as a link between the descriptive and
inferential statistics, methodologies for assessing and quantifying chance.
The objective of the course is to develop knowledge of the fundamental
probability tools for quantitatively determining the risk and assessing the
various problems encountered in decision making.
2 Prerequisites:
NIL
3 Student Learning Outcomes:
 The students will be able to distinguish between probability models
appropriate to different chance events and calculate probability according to
these methods.
 The course enables the students to develop the skill set to apply probability
theory in real life problems.1
Course Contents/Syllabus
4 Module I: Probability Space and Limit Theorems

5

6
Classes of Sets, Field, Sigma Field, Minimal Sigma Field, Borel 20
Sigma Field, Sequence of Sets, Limits of a Sequence of Sets,
Measure, Probability Measure, Definition of Probability, Important
Theorems on Probability, Conditional Probability, Baye’s Theorem,
and Independent Events.
Module II: Random Variables and Distribution Functions

Measurable Functions, Random variables and their Probability
30
Distributions, Distribution Functions and its Properties, Joint
Distribution of two Random Variables, Marginal and Conditional
Distributions, Expectation, Moments of Random Variables,
Important Inequalities concerning Expectation and Moments (Basic,
Markov’s, Chebychev’s, Kolmogorov’s, Holder’s, Minkowski’s,
Cauchy-Schwartz and Jensen’s inequalities),
Moment Generating Function, Probability Generating Function,
Characteristic Function, Characteristic Functions & their Properties,
Uniqueness Continuity and Inversion Theorems of Characteristic
Functions.
Module III: Convergence and Limit Theorems
 Convergence of a Sequence of Random Variables, Modes of
25
Convergence (convergence in probability, in distribution, almost
surely, and in the rth mean, monotone convergence theorem, Fatou’s
lemma, dominated convergence theorem), Relations among different
modes of convergence.
7
TOTAL
CREDIT
UNITS
4
Module IV: Law of Large Numbers and Central Limit Theorems
Laws of Large Numbers- Bernoulli’s, Chebyshev’s and Khinchine’s Weak 25
Law of Large Numbers, Strong Law of Large Numbers and Kolmogorov’s
theorem, Central limit theorem.
8
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a
separate Lab sessions. In addition to numerical applications, the real life problems
and situations will be assigned to the students and they are encouraged to get a
feasible solution that could deliver meaningful and acceptable solutions by the end
users. The focus will be given to incorporate probability and related measures to
develop a risk model for various applications.
9
Assessment/ Examination Scheme:
Theory L/T (%) Lab/Practical/Studio (%)
30%
NA
End Term Examination
70%
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
End Term
Examination
Components
(Drop
down)
MidTerm
Exam
Home
Assignment
Weightage
%)
10%
8%
Class
performance/
Viva
7%
Attendance
5%
70%
Textbooks
1. Rohatgi, V. K. and Saleh, A.K. Md. E. (2005). An Introduction to Probability and
Statistics, 2nd ed., John Wiley.
2. Biswas, S. and Srivastava, G. L. (2011). Mathematical Statistics, Narosa Publishing House,
New Delhi.
References:
1. Ash, Robert B. (2000). Probability and Measure Theory, Second Edition, Academic
Press, New York.
2. Loeve, M. (1978). Probability Theory, 4th Edition, Springer-Verlag.
3. Feller, W. (1968). An Introduction to Probability Theory and its Applications, 3 rd Edition,
Vol. I & II, John Wiley & Sons.
4. Goon, A.M., Gupta, M.K. and Dasgupta. B. (1985). An Outline of Statstical Theory, Vol.
I, World Press.
5. Uspensky, J.V. Introduction to Mathematical probability, Tata McGrow Hill & Sons.
6. Bhat, B.R. (1999). Modern Probability Theory, 3rd Edition, New Age International
Publishers.
7. Billingsley, P. (1986). Probability and Measure, 2nd Edition, John Wiley & Sons.
8. Capinski, M. and Zastawniah (2001). Probability through problems, Springer.
9. Chung, K. L. (1974). A Course in Probability Theory, 2nd Edition, Academic Press, New
York.
Annexure ‘AAB-CD-01’
Course Title: STATISTICAL METHODS
Course Code: STAT 613
Credit Units: 4
Level: PG
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Course Title
SW/F
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Weightage (%)
1
Course Objectives:

After studying the concept of random variable and distribution function in
probability theory, the knowledge of statistical distribution is of prime
need. It gives the idea about how the total probability is distributed among
the possible values of random variables. The main objective of the course
is to provide the detailed knowledge of the characterization of all the
useful distributions.
2 Prerequisites:
NIL
3 Student Learning Outcomes:

The students will be able to formulate the mathematical/statistical models
for real data set arising in various fields in order to analyze in respect of
various useful characteristics of the populations.
Course Contents/Syllabus
4 Module I: Random Variables and Distribution Function


5
6
7
Review of Random Variables and Probability Distribution
Theory. Convolution of Distribution Functions. Special types of
Distribution- Truncated, Compound and Censored.
Expectation, Moments of Random Variables. MGF, PGF,
Characteristic Functions.
Module II: Specific Distributions

Discrete Distributions – Bernoulli, Binomial, Poisson, Discrete Uniform,
Geometric, Negative Binomial and Hyper Geometric.

Continuous Distributions – Uniform, Exponential, Gamma, Beta, Chisquare, Weibull, Cauchy, Normal, Lognormal.

Characterization of Distributions, Characterization Properties of Normal
and some other distributions.

Truncated and Compound Distributions.
Module III: Regression and Correlation

Correlation Coefficient. Linear Regression. Rationale behind two Curves
of Regression. Relation between Correlation Coefficient and two
Regression Coefficients. Homoscedasticity of Linear Regression.

Bivariate Normal Regression. Multiple Regression and Multiple
Correlation. Multiple Correlation as Canonical Correlation.

Rank Correlation, Intra-class Correlation Coefficient.
Module IV: Sampling Distributions

Introducing Sampling Distributions, Methods of obtaining Sampling
Distributions.

Important sampling distributions - Chi-square, t and F. Applications of
these distributions in tests of significance. Non-central Chi-square, t and F
distributions and their properties.
TOTAL
CREDIT
UNITS
4
25
25
25
25
8
9
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a
separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate the
applications of order statistics and non-parametric methods for solving the real
life problems and cases.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
70%
End Term
Examination
MidTerm
Exam
Home
Assignment
CP/
Viva
Attendance
10%
8%
7%
5%
70%
Textbooks
1. Biswas, S. and Srivastava, G. L. (2011). Mathematical Statistics, Narosa Publishing House,
New Delhi.
2. Rohatgi, V. K. and Saleh, A. K. Md. E. (2005). An Introduction to Probability and Statistics.
2nd Edition, John Wiley and Sons.
Reference
1. Hogg, R.V., McKean, J. and Craig, A.T. (2012). Introduction to Mathematical Statistics.
Pearson Education.
2. Miller, I. and Miller, M. (2011). John E. Freund’s Mathematical Statistics. Prentice Hall.
Annexure ‘AAB-CD-01’
Course Title: Linear algebra and application
Course Code: STAT 615
Credit Units: 4
Level: PG
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Course Title
1
Course Objectives:
The motivation of introducing Linear Algebra course in Statistics is mainly to
study the basics of Algebra and also to study the distribution of several random
variables put together in bivariate, multivariate or in univariate with combination
of several independent random variables. The main objective to introduce this
course is to solve various problems by computing the inverse of a matrix, the
Unique Moore and Penrose generalized inverse methods.
Prerequisites:
NIL
Student Learning Outcomes:
2
3

SW/F
W
0
Weightage (%)
The students will learn about the basic concepts of vector space and linear
transformation.

The students will able to learn how to calculate Generalized Inverses of
matrices.
Course Contents/Syllabus
4 Module I:
Examples of vector spaces, vector spaces and subspace, independence in vector
spaces, existence of a Basis, the row and column spaces of a matrix, sum and
intersection of subspaces.
5 Module II:
Linear Transformations and Matrices, Kernel, Image, and Isomorphism, change
of bases, Similarity, Rank and Nullity.
6 Module III:
Inner Product spaces, orthonormal sets and the Gram-Schmidt Process, the
Method of Least Squares.
Basic theory of Eigen vectors and Eigen values, algebraic and geometric
multiplicity of eigen value, diagonalization of matrices, application to system of
linear differential equations .Factorization of Matrices
7 Module IV:
Generalized Inverses of matrices, Moore-Penrose generalized inverse. Real
quadratic forms, reduction and classification of quadratic forms, index and
signature, triangular reduction of a reduction of a pair of forms, Quadratic and
singular value decomposition, extrema of quadratic forms. Jordan canonical
form, vector and matrix decomposition.
8 Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a
separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are encouraged
to get a feasible solution that could deliver meaningful and acceptable solutions
by the end users. The focus will be given to incorporate the knowledge and
applications of reliability theory in industrial applications and problems solving.
9 Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term
Examination
TOTAL
CREDIT
UNITS
4
25
25
25
25
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
70%
End Term
Examination
MidTerm
Exam
Home
Assignment
CP/
Viva
Attendance
10%
8%
7%
5%
70%
Text:

Biswas, S. (1997): A Text Book of Matrix Algebra, 3rd Edition, Prentice Hall, New Delhi.
References:






Golub, G.H. and Van Loan, C.F.(1989): Matrix Computations, 2nd edition, John Hopkins University Press,
Baltimore-London.
Hadley, G. (1961). Linear Algebra. Addition-Wesley.
Nashed, M.(1976): Generalized Inverses and Applications, Academic Press, New York.
Robinson, D.J.S. (1991): A Course in Linear Algebra with Applications, World Scientific, Singapore.
Searle, S.R.(1982): Matrix Algebra useful for Statistics, John Wiley and Sons.
Strang, G.(1980): Linear Algebra and its Application, 2nd edition, Academic Press, London-New York.
Annexure ‘AAB-CD-01’
Course Title: Optimization Techniques and Applications
Course Code: STAT 621
Credit Units: 4
Level: PG
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Course Title
1
Course Objectives:
The objective of this course is to enhance the applications of optimization
techniques in engineering system and real life situations as well. The main aim
of this course is to present different methods to solve the constrained
optimization problems by using linear programming, integer linear
programming. In addition the use of optimization techniques is also explained
for network planning and scheduling.
Prerequisites:
NIL
Student Learning Outcomes:
2
3

The students will learn about the formulation of the given real life
problem as mathematical programming problem.

The students will acquire the knowledge for solving linear
programming problems and will able to interpret the results.

The students will able to minimize the transportation costs for the
transportation problems.
SW/F
W
0
TOTAL
CREDIT
UNITS
4
Weightage (%)
 The students will able to plan and schedule the network analysis.
Course Contents/Syllabus:
4 Module I:
Linear Programming Problems (LPP)
20
Introduction to LPPs, Solution of LPPs: Graphical Method & Simplex Method,
Use of Artificial Variables in simplex method: Charnes’ Big M method and Two
Phase Method, Duality in LPPs, Dual Simplex Method .
5 Module II:
Transportation Problems (TP)
30
Introduction to Transportation Problem, TP as a case of LPP, Methods to obtain
initial basic feasible solution to a TP: North West Corner Rule, Matrix Minima
Method, Vogel’s Approximation Method, Solution of the TP by MODI method,
Degeneracy in TPs, Unbalanced transportation problems and their solutions.
Assignment Problems (AP): Introduction to APs, AP as a complete degenerate
form of TP, Hungarian Method for solving APs, Unbalanced Assignment
problems and their solutions, APs with restrictions.
6 Module III:
Integer Linear Programming Problems
20
Integer Linear Programming Problems Mixed Integer Linear Programming
Problems, Cutting Plane Method, Branch and Bound Method. Sequencing
problem.
7 Module IV:
Project scheduling
30
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.
8
Probability of meeting the scheduled time. PERT Calculation, Distinctions
between CPM and PERT.
Pedagogy for Course Delivery:
9
The class will be taught using theory and practical methods using software in a
separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are encouraged
to get a feasible solution that could deliver meaningful and acceptable solutions
by the end users. The focus will be given to incorporate the knowledge and
applications of reliability theory in industrial applications and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
70%
End Term
Examination
MidTerm
Exam
HA
CP/
Viva
Attendance
10%
8%
7%
5%
70%
Text & References:






Hadley, G., “Linear Programming,”, Addison-Wesley, Mass.
Taha, H.A. “Operations Research – An Introduction”, Macmillian
F.S. Hiller, , G.J. Lieberman, ” Introduction to Operations Research”, Holden-Day
Harvey M. Wagner, “Principles of Operations Rsearch with Applications to Managerial
Decisions”, Prentice Hall of India Pvt. Ltd.
K. Swarup, P. K. Gupta and Man Mohan, “Operations Research”, Sultan Chand & Sons, New
Delhi.
Panneerselvam, “Operations Research” 2nd edition, PHI Pvt. Ltd.
Annexure ‘AAB-CD-01’
Course Title: Advanced Statistical Inference – I
Course Code: STAT 625
Credit Units: 4
Level: PG
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Course Title
1
Course Objectives:
In Statistics population parameters describe the characteristics under study.
These parameters need to be estimated on the basis of collected data called
sample. The purpose of estimation theory is to arrive at an estimator that exhibits
optimality. The estimator takes observed data as an input and produces an
estimate of the parameters. This course will make a student learn the various
properties of a good estimator as well as techniques to develop such estimators
from both classical and Bayesian point of view.
2
Prerequisites:
NIL
Student Learning Outcomes:
3

The students will able to learn about the various requirements to be a
good estimator.

The students will able to emphasize the statistical thinking.

The students will able to use technology by using various properties of
statistical inference.
SW/F
W
0
Weightage (%)

The students will able to distinguish the common elements of inference
procedures.
Course Contents/Syllabus
4 Module I:
Criterion of a good estimator- unbiasedness, consistency, efficiency and
sufficiency. Minimal sufficient statistics. Exponential and Pitman family of
distributions. Complete sufficient statistic, Koopman Darmaus’s exponential
form for complete sufficient statistic, Rao-Blackwell theorem, Lehmann-Scheffe
theorem, Cramer-Rao lower bound approach to obtain minimum variance
unbiased estimator (MVUE).
5 Module II:
Maximum likelihood estimator (mle), its small and large sample properties,
CAN & 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.
6
7
Module 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.
Module 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
TOTAL
CREDIT
UNITS
4
25
25
25
25
against one sided alternative hypothesis.
8
9
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a
separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are encouraged
to get a feasible solution that could deliver meaningful and acceptable solutions
by the end users. The focus will be given to incorporate the knowledge and
applications of reliability theory in industrial applications and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
70%
End Term
Examination
MidTerm
Exam
HA
CP/
Viva
Attendance
10%
8%
7%
5%
70%
Text & References:
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. Rohatgi, V.K. (1976): An introduction to Probability Theory and Mathematical Statistics, Wiley.
5. Biswas, S. and Srivastava, G. L. (2011). Mathematical Statistics, Narosa Publishing House,
New Delhi.
Annexure ‘AAB-CD-01’
Course Title: Advanced Sampling Theory
Course Code: STAT 632
Credit Units: 4
Level: PG
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Course Title
1
Course Objectives:
This course is designed to provide an overview of the theory and applications of
various sampling procedures in survey research methods. The objective of this
course is to emphasize the knowledge on survey process and the field of survey
research.
Prerequisites:
NIL
Student Learning Outcomes:
2
3

The students will able to learn various techniques used in sampling
practices.

The students will learn how to interpret the descriptive statistics for the
given data.
SW/F
W
0
Weightage
(%)

The students will able to conceptualize, conduct, interpret the statistical
analyses for the different population.
Course Contents/Syllabus
4
Module I:
Estimation of population mean, total and proportion in SRS and Stratified sampling. 25
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.
5
Module II:
Cluster sampling: Estimation of population mean and their variances based on 25
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.
6
7
8
Module III:
Two stage sampling: Estimation of population total and mean with equal and 25
unequal first stage units. Variances and their estimation. Optimum sampling and
sub-sampling fractions (for equal fsu’s only).
Module IV:
Double Sampling: Need for double sampling. Double sampling for ratio and 25
regression method of estimation.
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.
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a
separate Lab sessions. In addition to numerical applications, the real life problems
TOTAL
CREDIT
UNITS
4
9
and situations will be assigned to the students and they are encouraged to get a
feasible solution that could deliver meaningful and acceptable solutions by the end
users. The focus will be given to incorporate the knowledge and applications of
reliability theory in industrial applications and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
70%
End Term
Examination
MidTerm
Exam
HA
CP/
Viva
Attendance
10%
8%
7%
5%
70%
Text & References:
1. Cochran, W.G., (1977): Sampling Techniques, 3 rd edition, John Wiley.
2. Murthy, M.N. (1977): Sampling theory and methods. Statistical Publishing Society, Calcutta.
3. Sukhatme et al. (1984): Sampling theory of surveys with applications, Iowa state university press and
ISAS.
4. Singh, D. and Chaudhary, F.S. (1986): Theory and analysis of sample survey designs. New age
international publishers
Annexure ‘AAB-CD-01’
Course Title: Linear Models and Regression Analysis
Course Code: STAT 633
Credit Units: 4
Level: PG
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Course Title
1
Course Objectives:
This course focuses on building a greater understanding, theoretical
underpinning, and tools for applying the linear regression model and its
generalizations. With a practical focus, it explores the workings of multiple
regression and problems that arise in applying it, as well as going deeper into the
theory of inference underlying regression and most other statistical methods. The
course also covers new classes of models for binary and count data, emphasizing
the need to fit appropriate models to the underlying processes generating the data
being explained.
2
Prerequisites:
NIL
Student Learning Outcomes:
3

The students will learn the linear estimation and able to identify the best
linear unbiased estimator among various estimators.

The students will able to learn various tests of statistical hypotheses.

The students will know the differences between linear and nonlinear
models.
Course Contents/Syllabus
4 Module I: Fundamentals of Linear Estimation
Linear Model, Gauss-Markov Setup, LSE and GLSE, Estimable Functions, Best
Linear Unbiased Estimator (BLUE), Method of Construction of BLUE, Error
and Estimation Spaces, Normal Equations, Gauss-Markov Theorem and its
Applications (full rank and non-full rank), Theory of linear estimation based on
G-inverse, Quadratic Forms, Cochran’s Theorem and its Statistical
Interpretation, Expectation of Quadratic Forms.
5 Module II:
Test of Linear Hypothesis; ANOVA by linear estimation: One-way and two-way
classifications (one observation per cell and m observations per cell), Random
effect models (one-way and two-way classifications only), variance components.
6 Module III:
Linear Regression: Bivariate, Multiple, ANOVA; Extra Sum of Squares,
Orthogonal Columns, Partial and Sequential F-test, Testing of General Linear
Hypothesis, Bias in regression estimators, Minimum mean square prediction,
Test for equality of Regression Equations.
7 Module IV:
Non-Linear Models: Multi-collinearity, Ridge regression and principal
components regression, selecting best regression equation, Mallon’s Cp
Statistics.
8 Pedagogy for Course Delivery:
SW/F
W
0
TOTAL
CREDIT
UNITS
4
Weightage (%)
30
20
30
20
9
The class will be taught using theory and practical methods using software in a
separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are encouraged
to get a feasible solution that could deliver meaningful and acceptable solutions
by the end users. The focus will be given to incorporate the knowledge and
applications of reliability theory in industrial applications and problems solving.
Assessment/ Examination Scheme:
Theory
L/T (%)
Lab/Practical/Studio (%)
E
30%
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Comp
onent
s
(Drop
down)
Weig
htage
(%)
MidTerm
Exam
HA
CP/
Viva
10%
8%
7%
Attendance
5%
NA
End Term
Examinati
on
70%
Text & References:







Goon, A.M., Gupta, M.K. and Dasgupta, B. (1987): An Outline of Statistical Theory, Vol. 2, The World
Press Pvt. Ltd. Culcutta.
Rao, C.R. (1973): Introduction to Statistical Infererence and its Applications, Wiley Eastern.
Graybill, F.A. (1961): An introduction to linear Statistical Models, Vol. 1, McGraw Hill Book Co. Inc.
Draper, N.R. and Smith, H (1998): Applied regression Analysis, 3 rd Ed. Wiley.
Kshirsagar, A.M. (1983). A Course in Linear Models, Marcel Dekker, Inc., N.Y
Weisberg, S. (1985): Applied linear regression, Wiley.
Cook, R.D. and Weisberg, S. (1982): Residual and Inference in regression, Chapman & Hall.
Annexure ‘AAB-CD-01’
Course Title: Mathematical Demography
Course Code: [STAT 642]
Credit Units: 4
Level: PG
L
T
3
1
P/
S
#
Course Title
1
Course Objectives:
Mathematical Demography deals with the Population Analysis by building
Mathematical or Statistical models relating the growth of population by
investigating its components like Fertility, Mortality and Migration and builds up
Population Projection techniques. The applicability of the subject is very wide in
National planning is highly Significant. A student will get insight as to
mechanism that determines Population growth which is very useful in National
Planning as well as in Actuarial Science in solving Insurance problems.
2
Prerequisites:
NIL
Student Learning Outcomes:
3
4
5
6
7
8

The students will able to lean the basic concepts of mathematical
demography.

The students will able to construct the life table.

The students will learn about the risk theory.
SW/F
W
0
Weightage (%)
Module I:
Sources of Demographic data, Coverage and content errors in demographic data, 25
Chandrasekharan—Deming formula to check completeness of registration data,
adjustment of age data- use of Whipple, Myer and UN indices.
Module II:
Measures of mortality, description of life table, construction of complete and
abridged life tables, maximum likelihood, MVU and CAN estimators of life table
parameters. Model life table, Measures of fertility, Indices of fertility measures,
Relationship between CBR, GFR and TFR, Mathematical Models on fertility
Module III:
Population growth indices: measurement of population growth, logistic model,
methods of fitting logistic curves, Stable population analysis, Population
projection techniques, Frejka’s component method, Representation of component
method by the use of Leslie matrix.
Module IV:
Competing risk Theory: Measurement of competing risks, Inter-relations of the
death probabilities, Estimation of crude, net and partial crude probabilities of
death.
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a
TOTAL
CREDIT
UNITS
4
25
25
25
9
separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are encouraged
to get a feasible solution that could deliver meaningful and acceptable solutions
by the end users. The focus will be given to incorporate the knowledge and
applications of reliability theory in industrial applications and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
E
NA
MidTerm
Exam
HA
CP/
Viva
Attendanc
e
10%
8%
7%
5%
End Term
Examinati
on
70%
Text & References:






Samuel Preston, Patrick Heuveline, Michel Guillot (2000) Demography: Measuring and Modeling
Population Processes, Wiley-Blackwel.
Biswas, S. (1988): Stochastic Processes in Demography and Applications, Wiley Eastern Ltd.
Chiang, C.L. (1968): Introduction to Stochastic Processes in Bio statistics, John Wiley.
Keyfitz, N. (1971): Applied Mathematical Demography, Springer Verlag.
Spiegelman, M. (1969): Introduction to Demographic Analysis, Harvard University Press.
Kumar, R. (1986): Technical Demography, Wiley Eastern Ltd.
Annexure ‘AAB-CD-01’
Course Title: Advanced Biostatistics
Course Code: [STAT 643]
Credit Units: 4
Level: PG
L
T
3
1
P/
S
#
Course Title
1
Course Objectives:
To acquaint Public Health master and doctoral student with methods for analyzing
correlated data without requiring a high level of mathematical sophistication. The
course should we helpful in the analysis of research data and doctoral dissertation
projects.
Prerequisites:
NIL
Student Learning Outcomes:
2
3

SW/F
W
0
Weightage (%)
The students will able to use the applications of statistics in clinical data.

4
5
6
7
8
9
The students will able to interpret the results of the given data with the help
of different mathematical models.
Module I:
Survival analysis, Survival function and Hazard Function, Censoring, Type-I, Type-II
and Random Censoring, Progressively censored Type-I data, BLUE based on Type-II
censored data, Estimator for censored sample of ordered observation, basic concept of
some parametric, nonparametric and semiparametric survival models.
Module II:
Competing risk theory, Indices for measurement of probability of death under
competing risks and their inter-relations. Estimation of probabilities of death under
competing risks by maximum likelihood and modified minimum Chi-square methods.
Theory of independent and dependent risks.
Module III:
Stochastic epidemic models, Simple and general epidemic models (by use of random
variable technique), Carrier Borne Epidemic Model.
Module IV:
Planning and design of clinical trials; Phase I, II, and III trials; Consideration in
planning a clinical trial; designs for comparative trials; rules of allocation – Two
Armed Bandit Rule and Play The Winner Rule; Sample size determination in fixed
sample designs.
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a
separate Lab sessions. In addition to numerical applications, the real life problems and
situations will be assigned to the students and they are encouraged to get a feasible
solution that could deliver meaningful and acceptable solutions by the end users. The
focus will be given to incorporate the knowledge and applications of reliability theory
in industrial applications and problems solving.
Assessment/ Examination Scheme:
TOTAL
CREDIT
UNITS
4
25
25
25
25
Theory L/T (%)
Lab/Practical/Studio (%)
En
30%
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Componen
ts (Drop
down)
Weightage
(%)
NA
End Term
Examination
MidTerm
Exam
HA
CP/
Viva
Attendance
10%
8%
7%
5%
70%
Text & References:
 Collett, D. (2003): Modelling survival Data in Medical Research, Chapman & Hall/CRC.
 Cox, D.R. and Oakes, D. (1984). Analysis of Survival Data, Chapman Hall.
 Indrayan, A. (2008). Medical Biostatistics, Second Edition, Chapman & Hall/CRC.
 Lee, Elisa, T. (1992). Statistical Methods for Survival Data Analysis, John Wiley & Sons
 Ewens, W.J. and Grant, G.R. (2001). Statistical methods in Bio informatics: An introduction, Springer.
 David and Moeschberger. Theory of Competing Risks.
 Friedman, L.M., Furburg, C. and DeMets, D.L. (1998). Fundamentals of Clinical Trials, Springer Verlag.
Gross, A. J. and Clark V. A. (1975). Survival Distribution: Reliability Applications in Biomedical Sciences,
John Wiley & Sons.
Annexure ‘AAB-CD-01’
Course Title: Stochastic Processes and Applications
Course Code: [STAT 711]
Credit Units: 3
Level: PG
L
T
2
1
P/
S
#
Course Title
1
Course Objectives:
Stochastic process, or sometimes random process is a collection of random
variables; this is often used to represent the evolution of some random value, or
system, over time. Familiar examples of processes modeled as stochastic time series
include stock
market and exchange
rate fluctuations,
signals
such
as speech, audio and video, medical data such as a patient's EKG, EEG, blood
pressure or temperature,
and
random
movement
such
as Brownian
motion or random walks.
2
Prerequisites:
NIL
Student Learning Outcomes:
3

4
5
6
7
8
SW/F
W
0
Weightage (%)
The students will able to learn the basics of stochastic processes.
 The students will learn about the Renewal theory.
Module I:
Introduction to Stochastic Processes (sp’s); classification of sp’s according to state
space and time domain. Countable state Markov chains (MC’s), ChapmanKolmogorov equations, calculation of n-step transition probabilities and their limits.
Stationary distribution, classification of states, transient MC. Random walk and
gambler’s ruin problem. Applications of stochastic processes. Stationarity of
stochastic processes, autocorrelation, power spectral density function, power of a
process.
Module II:
Discrete state space continuous time MC, Kolmogorov- Feller differential
equations, Poisson process, birth and death process
Module III:
Renewal theory: Elementary renewal theorem and applications. Statement and uses
of key renewal theorem, study of residual lifetime process. Branching process:
Galton-Watson branching process, probability of ultimate extinction, distribution of
population size.
Module IV:
Martingale in discrete time, inequality, convergence and smoothing properties,
Queueing processes, application to queues –M/M/1 and M/M/C models.
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a
separate Lab sessions. In addition to numerical applications, the real life problems
and situations will be assigned to the students and they are encouraged to get a
feasible solution that could deliver meaningful and acceptable solutions by the end
users. The focus will be given to incorporate the knowledge and applications of
TOTAL
CREDIT
UNITS
3
30
20
30
20
9
reliability theory in industrial applications and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
E
30%
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
NA
End Term
Examination
MidTerm
Exam
HA
CP/
Viva
Attendance
10%
8%
7%
5%
70%
Text & References:












Medhi, J. (1994): Stochastic Processes, Wiley Eastern 2nd Ed.
Groos, Da Harris, C.M. (1985): Fundamental of Queuing Theory, Wiley.
Biswas, S. (1995): Applied Stochastic Processes, Wiley.
Adke, S.R. and Manjunath, S.M. (1984): An Introduction to Finite Markov Processes, Wiley Estern.
Bhat, B.R. (2000) : Stochastic Models: Analysis and Applications, New Age International, India. Chapter
13 (13.1-13.3).
Cinlar, E. (1975) : Introduction to Stochastic Processes, Prentice Hall.
Feller, W. (1968) : Introduction to Probability Theory and its Applications, Vol.1, Wiley Eastern.
Harris, T.E. (1963): The Theory of Branching Processes, Springer – Verlag.
Hoel, P.G., Port S.C. and Stone, C.J. (1972) : Introduction to Stochastic Processes, Houghton Miffin & Co.
Jagers, P. (1974) : Branching Processes with Biological Applications, Wiley.
Karlin, S. and Taylor, H.M. (1975) : A First Course in Stochastic Processes, Vol.1, Academic Press.
Parzen, E. (1962): Stochastic Processes, Holden – Day.
Annexure ‘AAB-CD-01’
Course Title: Statistical Quality Control
Course Code: [STAT 714]
Credit Units: 3
Level: PG
L
T
2
1
P/
S
#
Course Title
1
Course Objectives:
Quality Control is a comprehensive course in QC terminology, practices,
statistics, and troubleshooting for the clinical laboratory. Designed for those
who have little or no experience with quality control but need a firm grounding,
this course will help all students quickly and easily identify and correct errors
in quality control procedures. Concepts covered include: running assayed and
unassayed controls, specificity, sensitivity, Westgard rules, Levey-Jennings
charts, Youden plots, and CUSUM calculations. MediaLab also offers an
"Introduction to Quality Control" course to complement the more detailed and
thorough presentation in this course.
Prerequisites:
NIL
Student Learning Outcomes:
2
3

SW/F
W
0
Weightage (%)
The students will learn the basic concepts of quality control for
industrial purposes.

4
5
6
7
8
The students will able to construct various control charts for
monitoring the process control.
Module I:
Introduction to Statistical Quality Control, General theory and review of control
charts for attribute and variable data; OC and A. R. L. of control charts.
Some other control charts for variables - Moving Average and Moving Range
charts, Cusum charts ; Decision rules for Cusum charts - V-mark and decision
interval techniques, Equivalence of these two rules.
Module II:
Tolerance Range; Tolerance Range based on Order Statistics; Normal
Tolerance Range – Mean known, Variance unknown ; Mean unknown and
Variance known ; both Mean and Variance unknown.
Module III:
Acceptance Sampling, Lot Acceptance Sampling for Attributes Inspection,
Parameters of Acceptance Sampling Plan – AQL, LTPD, PR and CR;
Acceptance Sampling in terms of Testing of Hypotheses; characteristics of an
Acceptance Sampling Plan - OC function, ASN , AOQ. Single Sampling Plan –
Acceptance/Rejection Plan ; Corrective Sampling plan; Double Sampling plan;
Continuous Sampling plan. Single Sampling plan for Variable Inspection.
Module IV:
Process Capability Analysis, Capability Indices, Estimation, Cofidence
Intervals and Test of Hypothesis relating to capability indices for normally
distributed process characteristics.
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a
separate Lab sessions. In addition to numerical applications, the real life
TOTAL
CREDIT
UNITS
3
20%
20%
30%
30%
9
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate the
knowledge and applications of reliability theory in industrial applications and
problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
70%
End Term
Examination
MidTerm
Exam
HA
CP/
Viva
Attendance
10%
8%
7%
5%
70%
Text & References:
1. Montgomery, D. C. (1985): Introduction of Statistical Quality Control, Wiley.
2. Biswas, S. (2007). Statistics of Quality Control. New Central Book agency.
3. Ott, E. R. (1975): Process Quality Control. McGraw Hill.
Annexure ‘AAB-CD-01’
Course Title: Advanced Statistical Inference – II
Course Code: [STAT 701]
Credit Units: 4
Level: PG
L
T
3
1
P/
S
#
Course Title
1
Course Objectives:
In Statistics population parameters describe the characteristics under study.
These parameters need to be estimated on the basis of collected data called
sample. The purpose of estimation theory is to arrive at an estimator that exhibits
optimality. The estimator takes observed data as an input and produces an
estimate of the parameters. This course will make a student learn the various
properties of a good estimator as well as techniques to develop such estimators
from both classical and Bayesian point of view.
2
Prerequisites:
NIL
Student Learning Outcomes:
3
4
5
6
7

The students will able to emphasize the statistical thinking in decision
theory.

The students will able to use technology by using various properties of
statistical inference.

The students will able to distinguish the common elements of inference
procedures.
Module I:
Statistical decision problem: Decision problem and 2-person game, nonrandonized, mixed and randomized decision rules, loss function, risk function,
admissibility, Bayes rules, minimax rules, least favourable distributions,
complete class and minimal complete class.
Module II:
Decision problem for finite parameter space, convex loss function. Admissible
Bayes & minimax estimators, Test of simple hypothesis against a simple
alternative from decision theoretic vew point..
Module III:
Bayes theorem and computation of posterior distribution, Bayesian point
estimation as a prediction problem from posterior distribution, Bayes estimators
for (i) absolute loss function (ii) squared loss function and (iii) 0-1 loss function,
Evaluation of estimates in terms of the posterior risk.
Module IV:
SW/F
W
0
Weightage (%)
25
25
25
Bayesian interval estimation, Bayesian testing of hypothesis, Bayes factor 25
for various types of testing hypothesis problem depending upon whether
the null hypothesis and the alternative hypothesis are simple or
composite, Bayesian prediction problem.
8
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a
TOTAL
CREDIT
UNITS
4
separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are encouraged
to get a feasible solution that could deliver meaningful and acceptable solutions
by the end users. The focus will be given to incorporate the knowledge and
applications of reliability theory in industrial applications and problems solving.
Assessment/ Examination Scheme:
9
Theory L/T (%)
Lab/Practical/Studio (%)
30%
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
En
NA
MidTerm
Exam
HA
CP/
Viva
Attendanc
e
10%
8%
7%
5%
End Term
Examinati
on
70%
Text & References:




Farguson, T.S. (1967), Mathematical Statistics Academic.
Goon, A.M., Gupta M.K. and Dasgupta, B. (1973): An Outline of Statistical Theory, Vol.2, World Press.
Berger, J.O.: Statistical Decision theory and Bayesian Analysis, Springer-Verlag
Sinha, S.K. (1998): Bayesian Estimation, New Age International
Annexure ‘AAB-CD-01’
Course Title: Experimental Design
Course Code: [STAT 634]
Credit Units: 4
Level: PG
L
T
3
1
P/
S
SW/F
W
#
Course Title
1
Course Objectives:
The course objective is to learn how to plan, design and conduct experiments efficiently
and effectively, and analyze the resulting data to obtain objective conclusions. Both
design and statistical analysis issues are discussed. Opportunities to use the principles
taught in the course arise in all phases of engineering work, including new product design
and development, process development, and manufacturing process improvement.
Applications from various fields of engineering (including chemical, mechanical,
electrical, materials science, industrial, etc.) will be illustrated throughout the course.
Computer software packages (Design-Expert, Minitab) to implement the methods
presented will be illustrated extensively, and you will have opportunities to use it for
homework assignments and the term project.
2
Prerequisites:
NIL
Student Learning Outcomes:
3
4
5
6
7
8

The students will able to learn about basic principles of design of experiments.

The students will able to do various experimental design for the given data.

The students will learn the analysis of series experiments.
Module I:
Review of linear estimation and basic designs; ANOVA: Fixed effect models (2-way
classification with unequal and proportional number of observations per cell); Random
and Mixed effect models (2-way classification with m (>1) observations per cell);
ANCOVA for RBD; Missing plot technique.
Module II:
Incomplete Block Designs; Concepts of Connectedness, Orthogonality and Balancing;
Intrablock Analysis of General Incomplete Block design; Balanced Incomplete Block
Designs (BIBD) with and without recovery of interblock information; PBIBD. Lattice
Design.
Module III:
Factorial Experiments: 2n, 32 and 33 systems only. Complete and Partial Confounding.
Factorial Replication in 2n systems. Split plot design.
Module IV:
Finite fields. Finite Geometries- Projective geometry and Euclidean geometry.
Construction of complete set of mutually orthogonal latin squares. Construction of
B.I.B.D. using finite Abelian groups, MOLS, finite geometry and method of differences.
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a separate
Lab sessions. In addition to numerical applications, the real life problems and situations
0
TOTAL
CREDIT
UNITS
4
Weightage (%)
20%
30%
30%
20%
9
will be assigned to the students and they are encouraged to get a feasible solution that
could deliver meaningful and acceptable solutions by the end users. The focus will be
given to incorporate the knowledge and applications of reliability theory in industrial
applications and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
End
End Term
Examination
Mid-Term
Exam
HA
CP/
Viva
Attendance
10%
8%
7%
5%
70%
Text & References:
1. Das, M.N. and Giri, N.C. (1986). Design and Analysis of Experiments, Wiley Eastern.
2. Chakrabarti, M.C. (1962). Mathematics of Design and Analysis of Experiments, Asia
Publishing House, Bombay.
3. Dey, A. (1986). Theory of Block Designs, John Wiley & Sons.
4. Montgomery, D.C. (2005). Design and Analysis of Experiments, Sixth Edition, John Wiley.
5. Raghavarao, D. (1970). Construction and Combinatorial Problems in Design of Experiments,
John Wiley & Sons.
6. Giri, N. (1986). Analysis of Variance. South Asian Publishers.
Annexure ‘AAB-CD-01’
Course Title: Survival Analysis
Course Code: [STAT 715]
Credit Units: 3
Level: PG
L
T
2
1
P/
S
#
Course Title
1
Course Objectives:
Survival Analysis is a collection of methods for the analysis of data that involve
the time to occurrence of some event, and more generally, to multiple durations
between occurrences of different events or a repeatable (recurrent) event. From
their extensive use over decades in studies of survival times in clinical and health
related studies and failures times in industrial engineering (e.g., reliability
studies), these methods have evolved to special applications in several other
fields, including demography (e.g., analyses of time intervals between successive
child births), sociology (e.g., studies of recidivism, duration of marriages), and
labor economics
(e.g., analysis of spells of unemployment, duration of strikes).
2
Prerequisites:
NIL
Student Learning Outcomes:
3
4
5
6
7
8

The students will able to learn the basic concepts of survival analysis.

The students will able to study different life distributions for research
purposes.
 The students will learn how to estimate the survival function.
Module I:
Concepts of Censoring: Type-I, Type-II and random censoring; likelihood in
these cases. Parametric - exponential, gamma, Weibull, lognormal, Pareto,
Rayleigh, logistic and log-logistic; Life distributions, linear failure rate.
Inference for exponential, gamma, Weibull distributions under censoring.
Module II:
Non-parametric – Life Table method, Greenwood’s method, Kaplan-Meier,
Nelson-Aalen; Concept of Self-consistency and EM algorithm, Robust
Estimators, L-estimators and M-estimators, Baye’s estimators
Module III:
Nonparametric Comparision of Survival Curves: Gehan test, Log-rank test.
Mantel-Haenszel test, Efron’s test.
Module IV:
Semi-parametric Models: Cox proportional hazard model. Accelerated Failure
Time Model.
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a
separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are encouraged
to get a feasible solution that could deliver meaningful and acceptable solutions
by the end users. The focus will be given to incorporate the knowledge and
applications of reliability theory in industrial applications and problems solving.
SW/F
W
0
TOTAL
CREDIT
UNITS
3
Weightage (%)
25
25
25
25
9
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
MidTerm
Exam
HA
CP/
Viva
Attendance
10%
8%
7%
5%
En
NA
End Term
Examinatio
n
70%
Text & References:






Cox, D.R. and Oakes, D. : Analysis of Survival Data, Chapters 1, 2, 3, 4.
Crowder Martin, J. (2001): Classical Competing Risks, Chapman & Hall, CRC, London.
Gross, A.J. & Clark, V.A.: Survival Distributions-Reliability Applications in Biomedical Sciences,
Chapters 3,4.
Elandt-Johnson, R.E. and John, N.L.: Survival Models and Data Analysis, John Wiley and Sons.
Miller, R.G. (1981): Survival Analysis, Chapters 1-4.
Kalbfleisch, J.D. and Prentice, R.L. (1980): The Statistical Analysis of Failure Time Data, John Wiley.
Annexure ‘AAB-CD-01’
Course Title: Theory of Econometrics
Course Code: Yet to be decided
Credit Units: 3
Level: PG
L
T
2
1
P/
S
#
Course Title
1
Course Objectives:
A significant development of Mathematical Economics is the increased
application of probabilistic tools and Statistical techniques known as
“Econometrics”.
A reasonable understanding of econometric principles is indispensable for
further studies in economics. This course is aimed at introducing students to the
most fundamental aspects of both mathematical economics and econometrics.
The objective of this paper is to apply both deterministic as well as Stochastic
models for the purpose of Planning. The techniques of estimation in
Econometrics like’ two or three stage Least squares’ are entirely non traditional
than that of classical estimation in Statistics. With the knowledge of the
contents of this paper students will acquire how Modern Statistics answers
Economic problems.
2
Prerequisites:
Graduate level knowledge of elementary Algebra and Estimation Theory
Student Learning Outcomes:
3

The students will able to apply the basic concepts of economics for
interpreting the results of the given data.

The students will able to acquire knowledge on various econometric
methods and techniques.
SW/F
W
0
Weightage (%)

4
5
6
Enable students to conduct statistical analysis of different economic
dataset.
Module I:
Introduction of Theory of Econometrics. Nature and Scope of
Econometrics. Meaning, Scope, and Limitations. Methodology of
econometrics. Types of data: Time series, Cross section and panel data.
General Linear Model – Assumptions, least square estimation. The correlation
Matrix, Pridiction, linear restrictions, Multi-Collinearity and.
Specification Error
Module II:
Generalised Least squares-the generalized Least Square(Aitken) estimator,
Heteroscedasticitic disturbances, pure and mixed estimation, grouping of
observations, grouping of observations.
Autocorrelation – nature of autocorrelation, consequences of autocorrelated
disturbances, conventional tests for autocorrelation, Theil’s BLUE procedure,
estimation, prediction.
Module III:
Errors in Variables, time as a variable, Dummy variable, Estimation from
grouped data. Lagged variables and distributed Lag Models-Exogenous, &
Endogenous lagged variables, Methods of estimation of lagged models.
Simultaneous equation Models and methods. ILS, 2SLS, and least variance
TOTAL
CREDIT
UNITS
3
20%
30%
30%
7
8
9
ratio. The problem of Identification, Implications of the identification state of a
model, formal rues for identification, Identifying restrictions, test for
identifying restrictions. Restriction on structural parameters, restrictions on
variances and covariaces.
Module IV:
Mathematical representation of economic models, demand function, supply
function, utility function, production function, cost function, revenue function,
profit function, saving function, investment function. MPC, marginal utility,
MPS, Marginal product, marginal cost, marginal revenue, marginal rate of
substitution, Relationship between average revenue and marginal revenue,
relationship between average cost and marginal cost. Concept of elasticitydemand elasticity, price elasticity, income elasticity and cross elasticity-Angel
function.
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a
separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
20
10%
8%
NA
End Term
Examination
HA
MidTerm
Exam
E
CP/
Viva
Attendance
7%
5%
70%
Text & References:
 Chiang A.C. and K. Wainwright, Fundamental Methods of Mathematical Economics, 4 th Edition, McGrawHill, New York, 2005.
 Dowling E.T, Introduction to Mathematical Economics, 2nd Edition, Schaum’s Series, McGraw- Hill, New
York, 2003(ETD)
 Damodar N.Gujarati, Basic Econometrics, McGraw-Hill, New York.
 Johnston, J., Econometric Methods, 2nd edition, McGraw-Hill, 1972
 Koutsoyiannis A. Theory of Econometrics(2nd edition), ELBS
 Goldberger, A.S.,(1991), A Course in Econometrics. Cambridge, MA: Harvard University Press.
 Wooldridge Introductory Econometrics(3rd edition), Thomson
 Greene, W.(1997), Econometric Analysis
 Henderson and Quandt, Microeconomic Theory, McGraw Hill Company, New York.
 Lange Oscar, Introduction to Econometrics.
 Mathematical Economics by Bush , clown.
Annexure ‘AAB-CD-01’
Course Title: Modeling and Simulation
Course Code: [STAT 722]
Credit Units: 4
Level: PG
L
T
3
1
P/
S
#
Course Title
1
Course Objectives:
Modeling and simulation is getting information about how something will
behave without actually testing it in real life. For instance, if we wanted to design
a racecar, but weren't sure what type of spoiler would improve traction the most,
we would be able to use a computer simulation of the car to estimate the effect of
different spoiler shapes on the coefficient of friction in a turn. We're getting
useful insights about different decisions we could make for the car without
actually building the car.
Prerequisites:
NIL
Student Learning Outcomes:
2
3
4
5
6
8

The students will able to learn basic concepts of modeling and about the
formulation of the mathematical model.

The students will able to do comparative study of different populations
by using simulation.
SW/F
W
0
TOTAL
CREDIT
UNITS
4
Weightage (%)
Module I:
Introduction to Simulation modeling, Mathematical Models, types of 25
Mathematical models and properties, Discrete Simulation model, Continuous
Simulation, Monte-Carlo simulation.
Module II:
Approaches to differential equation: Heun method, Local stability theory: 25
Bernoulli Trials, Classical and continuous models, Case studies in problems of
engineering and biological sciences.
Module III:
Stochastic Simulation, Selecting Input Probability Distributions, Random 25
Number generation, Techniques for Generating Continuous Random Variates,
Generating Discrete Random Variates, simulating a non – homogeneous Poisson
Process and queuing system.
Module IV:
Introduction to Markov Chain Monte Carlo (MCMC), MCMC Basics-- 25
Metropolis, Metropolis-Hastings, and Gibbs Sampling, Convergence and Exact
sampling techniques, A variety of tricks for MCMC design.
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a
separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are encouraged
to get a feasible solution that could deliver meaningful and acceptable solutions
by the end users. The focus will be given to incorporate the knowledge and
applications of reliability theory in industrial applications and problems solving.
9
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
E
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
End Term
Examination
MidTerm
Exam
HA
CP/
Viva
Attendance
10%
8%
7%
5%
70%
Text & References:
 Edward A. Bender. An Introduction to Mathematical Modeling.
 A. C. Fowler. Mathematical Models in Applied Sciences, Cambridge University Press.
 Seila Andrew F.; Ceric Vlatko and Tadikamalla Pandu. Applied Simulation Modeling, Cengage Learning.
 Winston Wayne L. Probability Models, Cengage Learning.
 J. N. Kapoor. Mathematical Modeling, Wiley eastern limited.
 S.M. Ross. Simulation, India Elsevier Publication.

A.M. Law and W.D. Kelton. Simulation Modeling and Analysis, T.M.H. Edition.
Annexure ‘AAB-CD-01’
Course Title: Reliability Theory and Applications
Course Code: [STAT 725]
Credit Units: 4
Level: PG
L
T
3
1
P/
S
#
Course Title
1
Course Objectives:
Reliability Course is a practical application of fundamental mechanical
engineering to system and component reliability. Designed for the practitioner,
this course covers the theories of mechanical reliability and demonstrates the
supporting mathematical theory. For the beginner, the essential tools of
reliability analysis are presented and demonstrated. These applications are
further solidified by practical problem solving and open discussion. With the
knowledge of the contents of the paper the students will be able to apply this
branch of Engineering Statistics very fruitfully in industrial applications.

Prerequisites:
NIL
Student Learning Outcomes:
2
3
4
5
6
7
8

The students will learn how to construct the systems for getting the
maximum reliability.

The students will able to use different distributions for the study of
systems.
 The students will able to construct Life cycle curves.
Module I:
Definition of Reliability function, hazard function & failure rate, pdf in form of
Hazard function, Reliability function and mean time to failure distribution
(MTTF) with DFR and IFR. Basic characterstics for exponential, normal and
lognormal, Weibull and gamma distribution, Loss of memory property of
exponential distribution
Module II:
Life cycle curves and probability distribution in modeling reliability, Reliability
of the system with independent limit connected in (a) Series (b) parallel and (c)
K out of n system.
Module III:
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)].
Module IV:
Accelerated testing, types of acceleration and stress loading. Life stress
relationships. Arrhenius –lognormal, Arrhenius-Weibull, Arrhenius-exponential
models, Power-Weibull and Power-exponential models
Pedagogy for Course Delivery:
SW/F
W
0
TOTAL
CREDIT
UNITS
4
Weightage (%)
25
25
25
25
9
The class will be taught using theory and practical methods using software in a
separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are encouraged
to get a feasible solution that could deliver meaningful and acceptable solutions
by the end users. The focus will be given to incorporate the knowledge and
applications of reliability theory in industrial applications and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
70%
End Term
Examination
MidTerm
Exam
HA
CP/
Viva
Attendance
10%
8%
7%
5%
70%
Text & References:
1.
2.
3.
4.
Sinha,S.K. (1980): Reliability and life testing, Wiley,Eastern Ltd.
Nelson, W. (1989): Accelerated Testing, Wiley.
Zacks: Introduction to reliability analysis, probability models and statistical, Springer-Verlag.
Barlow, R.E. and Proschan, F. (1965) Mathematical Theory of Reliability, Wiley, New York,
NY.
5. Barlow, R.E. and Proschan, F. (1975) Statistical Theory of Reliability, Holt, Rinehart &
Winston, New York, NY.
Annexure ‘AAB-CD-01’
Course Title: ACTUARIAL STATISTICS
Course Code: Yet to be decided
Credit Units: 4
Level: PG
L
T
3
1
P/
S
#
Course Title
1
Course Objectives:
Actuarial Science is the discipline that applies mathematical and statistical
methods to assess risk in the insurance and finance industries. In view of the
uncertainties involved, probability theory, statistics and economic theories
provide the foundation for developing and analysing actuarial models. Using
an appropriate stochastic model, simulation and high speed computing, it has
become possible to construct various tables and objectively determine the
premiums of different types of insurance contracts, even in the presence of
uncertainties associated with the prevailing risk factors. In such a decision
making process, statistical techniques play a central role. A strong statistical
background provides a good foundation for the integrated aspects of finance,
economics, risk management and insurance.
2
Prerequisites:
NIL
Student Learning Outcomes:
3
4
5
6

The students will acquire the knowledge on various statistical
techniques in insurance field.

The students will able to compute risks for the given real life
situation.

The students will learn about the Life annuities.
Module I:
Utility theory, insurance and utility theory, models for individual claims and
their sums, survival function, curt ate future lifetime, force of mortality. Life
table and its relation with survival function, examples. Multiple life functions,
joint life and last survivor status.
Module II:
Multiple decrement models, deterministic and random survivorship groups,
associated single decrement tables, central rates of multiple decrements.
Distribution of aggregate claims, compound Poisson distribution and its
applications. Claim Amount distributions, approximating the individual
model, Stop-loss insurance.
Module III:
Principles of compound interest: Nominal and effective rates of interest and
discount, force of interest and discount, compound interest, accumulation
factor.
Life insurance: Insurance payable at the moment of death and at the end of the
year of death-level benefit insurance, endowment insurance, deferred
insurance and varying benefit insurance.
Life annuities: Single payment, continuous life annuities, discrete life
annuities, life annuities with monthly payments, varying annuities.
SW/F
W
0
Weightage (%)
25
25
25
TOTAL
CREDIT
UNITS
4
7
8
9
Module IV:
Net premiums: Continuous and discrete premiums, true monthly payment
premiums.
Net premium reserves: Continuous and discrete net premium reserves,
reserves on a semi continuous basis, reserves based on true monthly
premiums.
Lab
Problems based on All papers of Semester IV
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in
a separate Lab sessions. In addition to numerical applications, the real life
problems and situations will be assigned to the students and they are
encouraged to get a feasible solution that could deliver meaningful and
acceptable solutions by the end users. The focus will be given to incorporate
the knowledge and applications of reliability theory in industrial applications
and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
25
Lab/Practical/Studio (%)
30%
E
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
End Term
Examination
MidTerm
Exam
HA
CP/
Viva
Attendance
10%
8%
7%
5%
70%
Text & References:



N.L. Bowers, H.U. Gerber J.C. Hickman, D.A. Jones Mand C.J. Nesbitt, (1986): ‘Actuarial Mathematics’,
Society of Actuarial, Mathematics’, Society for Actuarial, Ithaca, Illinois, U.S.A. Second Edition (1997).
Section I – Chapters: 1,2,3,8,9,11, 13. Section II – Chapters: 4,5,6,7.
Spurgeon E.T. (1972) : Life Contingencies, Cambridge University Press.
Neill, A. (1977) : Life Contingencies, Heineman.
Annexure ‘AAB-CD-01’
Course Title: Multivariate Analysis
Course Code: [STAT 705]
Credit Units: 4
Level: PG
L
T
3
1
P/
S
#
Course Title
1
Course Objectives:
Multivariate analysis is the analysis of observations on several correlated random
variables for a number of individuals in one or more samples simultaneously, this
analysis, has been used in almost all scientific studies. For example, the data may
be the nutritional anthropometrical measurements like height, weight, arm
circumference, chest circumference, etc. taken from randomly selected students to
assess their nutritional studies. Since here we are considering more than one
variable this is called multivariate analysis.
2
Prerequisites:
NIL
Student Learning Outcomes:
3

SW/F
W
0
Weightage (%)
The students will learn various statistical techniques for multivariate data.

4
The students will able to do analysis by using different procedures for
multivariate data.
Module I:
Singular and non-singular multivariate normal distributions, Characteristic
function of N p (  , ) Maximum likelihood estimators of  and  in
25
N p (  , ) and their independence.
5
6
7
8
Module II:
Wishart distribution: Definition and its distribution, properties and characteristic
function. Generalized variance. Testing of independence of sets of variates and
equality of covariance matrices.
Estimation of multiple and partial correlation coefficients and their null
distribution, Test of hypothesis on multiple and partial correlation coefficients.
Module III:
Hotelling’s
: 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
. Discriminant analysis:
Classification of observations into one or two or more groups. Estimation of the
misclassification probabilities. Tests associated with discriminant functions.
Module IV:
Principal component, canonical variate and canonical correlation: Definition, use,
estimation and computation. Cluster analysis, Factor Analysis.
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a
separate Lab sessions. In addition to numerical applications, the real life problems
and situations will be assigned to the students and they are encouraged to get a
feasible solution that could deliver meaningful and acceptable solutions by the end
users. The focus will be given to incorporate the knowledge and applications of
reliability theory in industrial applications and problems solving.
TOTAL
CREDIT
UNITS
4
25
25
25
9
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
E
30%
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Component
s (Drop
down)
Weightage
(%)
NA
End Term
Examination
MidTerm
Exam
HA
CP/
Viva
Attendance
10%
8%
7%
5%
70%
Text & References:
 Anderson, T.W. (1984): An introduction to multivariate statistical analysis. John Wiley.
 Giri, N.C. (1977): Multivariate statistical inference. Academic Press.
 Singh, B.M. (2002): Multivariate statistical analysis. South Asian Publishers.
 Johnson A. Richard and Wichern dean W. Applied Multivariate Statistical Analysis(2 nd Indian reprint
2005), Pearson Education
Annexure ‘AAB-CD-01’
Course Title: Statistical Genetics
Course Code: [STAT 724]
Credit Units: 4
Level: PG
L
T
3
1
P/
S
#
Course Title
1
Course Objectives:
The goal of the program is to provide an opportunity for Students will receive an
in depth training in the statistical foundations and methods of analysis of genetic
data, including genetic mapping, quantitative genetic analysis, and design and
analysis of medical genetic studies. They will learn Population Genetics theory
and Computational Molecular Biology. Those not already having the necessary
background will also study some basic Genetics courses.
The primary goal of the program is to provide an opportunity for students from the
Mathematical, Statistical, and Computational Sciences to learn to use their skills in
the arena of molecular biology and genetic analysis.
2
Prerequisites:
NIL
Student Learning Outcomes:
3
4
5
6
7

The students will acquire the knowledge on the applications of statistics
in life sciences.

The sudents will able to do various statistical analyses for the given
biological data.
Module I:
Functions of survival time, survival distributions and their applications viz.
exponential, gamma, weibull, Rayleigh, lognormal, death density function for a
distribution having bath-tub shape hazard function. Tests of goodness of fit for
survival distributions (WE test for exponential distribution, W-test for lognormal
distribution, Chi-square test for uncensored observations).
Module II:
Competing risk theory, Indices for measure-ment of probability of death under
competing risks and their inter-relations. Estimation of probabilities of death under
competing risks by maximum likelihood and modified minimum Chi-square
methods. Theory of independent and dependent risks. Bivariate normal dependent
risk model. Conditional death density functions. Stochastic epidemic models:
Simple and general epidemic models (by use of random variable technique).
Module III:
Basic biological concepts in genetics, Mendels law, Hardy- Weinberg
equilibirium, random mating, distribution of allele frequency ( dominant/codominant cases), Approach to equilibirium for X-linked genes, natural selection,
mutation, genetic drift, equilibirium when both natural selection and mutation are
operative, detection and estimation of linkage in heredity.
Module IV:
Planning and design of clinical trials, Phase I, II, and III trials. Consideration in
SW/F
W
0
TOTAL
CREDIT
UNITS
4
Weightage (%)
25
25
25
25
planning a clinical trial, designs for comparative trials. Sample size determination
in fixed sample designs.
8
9
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using software in a
separate Lab sessions. In addition to numerical applications, the real life problems
and situations will be assigned to the students and they are encouraged to get a
feasible solution that could deliver meaningful and acceptable solutions by the end
users. The focus will be given to incorporate the knowledge and applications of
reliability theory in industrial applications and problems solving.
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
E
NA
End Term
Examination
MidTerm
Exam
HA
CP/
Viva
Attendance
10%
8%
7%
5%
70%
Text & References:













Biswas, S. (1995). Applied Stochastic Processes. A Biostatistical and Population Oriented Approach, Wiley
Eastern Ltd.
Collett, D. (2003). Modelling Survival Data in Medical Research, Chapman & Hall/CRC.
Cox, D.R. and Oakes, D. (1984). Analysis of Survival Data, Chapman and Hall.
Elandt Johnson R.C. (1971). Probability Models and Statistical Methods in Genetics, John Wiley & Sons.
Ewens, W. J. (1979). Mathematics of Population Genetics, Springer Verlag.
Ewens, W. J. and Grant, G.R. (2001). Statistical methods in Bio informatics: An Introduction, Springer.
Friedman, L.M., Furburg, C. and DeMets, D.L. (1998). Fundamentals of Clinical Trials, Springer Verlag.
Gross, A. J. And Clark V.A. (1975). Survival Distribution; Reliability Applications in Biomedical Sciences,
John Wiley & Sons.
Indrayan, A. (2008). Medical Biostatistics, Second Edition, Chapman & Hall/CRC.
Lee, Elisa, T. (1992). Statistical Methods for Survival Data Analysis, John Wiley & Sons.
Li, C.C. (1976). First Course of Population Genetics, Boxwood Press.
Miller, R.G. (1981). Survival Analysis, John Wiley & Sons.
Robert F. Woolson (1987). Statistical Methods for the analysis of biomedical data, John
Wiley & Sons.
Annexure ‘AAB-CD-01’
Course Title: Mathematical Statistics
L
T
P/
S
SW/F
W
Course Code:
Credit Units: 5
Level: M. Sc.(P.G)
3
1
2
0
TOTAL
CREDIT
UNITS
5
Please give your valuable feedback ratings (on the scale of 6 points) for following course
curriculum with respect to relevance to Industry / Profession:
6
Excellent
5
Very
Good
4
Good
3
Moderate
#
Course Title
1
Course Objectives:
The main objective of the course is to provide the
detailed knowledge of the random variable and its
applications to various probability distributions. Also
illustrate the use of basic statistical tools to analyze the
given data and interpretation.
2
Prerequisites:
NILL
Student Learning Outcomes:
3

The students will be able to calculate moments,
moment generating function characteristic
function, random variables and distribution
functions.

The students will learn to get the solution of the
problems based on probability distribution.

The students will learn to get the solution of the
problems based statistical inference.
2
Needs
Improvement
Comment
s (if any)

The students will learn to get the solution of the
problems based on correlation and regression.
Course Contents / Syllabus:
4 Module I Random variable and mathematical expectation
1
Poor
20%
Weightag
e
5
6
Set of events. Operation on sets, sequences of sets and their
limits, Random variables and Distribution functions.
Probability density function, Probability mass function.
Mathematical Expectation, Expectation of a function of a
random variable, conditional expectation, Moments of a
random variable, variance and covariance of a random
variable. Moment Generating function, Characteristic function,
Probability generating function.
Module II Probability distributions
30%
Weightag
e
Discrete distributions: Bernoulli, Binomial, Poisson,
Geometric, Negative Binomial, uniform, Hypergeometric and
various properties. Computation mean and variance through
moment generating function. Fitting of Binomial and Poission
distribution.
Continuous distributions: Uniform, exponential, Gamma
distribution, Beta distribution, Normal distribution.
Computation mean and variance through moment generating
function. Fitting of Normal distribution.
Module III Statistical Inference
35%
Weightag
e
Introduction to statistical inference, Population, sample,
parameter, Statistic and Estimator. Requirements of a good
estimator: Unbiasedness, Consistency, Sufficiency, C.R.
inequality and efficiency. Minimal sufficient statistics.
Exponential and Pitman family of distributions. Complete
sufficient statistic, Rav-Blackwell theorem, Lehmann-Scheffe
theorem.
Methods of Estimation: Method of Moments, Method of
Maximum Likelihood and its small sample properties, CAN &
BAN estimators, .
7
Module IV Test of significance and Regression Analysis
Test of significance based on Normal distribution, Student tdistribution, Test of single mean, difference of two means,
Paired t-test, Chi-square, F-test and Analysis of variance
(ANOVA) one way classification.
8
Scatter diagram, Correlation, types of correlation, Spearman’s
rank correlation and properties of correlation. Linear
Regression, lines of regressions and regression coefficients.
Introduction of Partial and Multiple correlation and properties
of residuals.
Pedagogy for Course Delivery:
1. All the topics covered in the syllabus will be correlated
15%
Weightag
e
with its applications in real life situations and also in
other disciplines.
2. Extra sessions for revision will be undertaken.
1
1
Assessment/ Examination Scheme:
Theory L/T
(%)
Lab/Practical/Studio
(%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal
Assessment
Component
Mid- H CP/ Attendanc
s (Drop
Term
A Viv
e
down)
Exa
a
m
Weightage
(%)
10%
8%
7%
5%
70%
End Term
Examinatio
n
70%
Text & References:
1. Feller,W.(1971): Introduction to Probability Theory and its Applications, Vol. I and
II. Wiley Eastern-Ltd.
2. V. K. Rohatgi, (1984): An Introduction to Probability Theory and Mathematical
Statistics, Wiley Eastern.
3. Hogg, R.V. and Craig, A.T.(1971): Introduction to Mathematical Statistics, McMillan.
4. Mood, A.M., Graybill,F.A. and Boes, D.C.(1974): Introduction to the Theory of
Statistics, McGraw Hill.
6. Gupta and Kapoor (2013): Fundamentals of Mathematical Statistics, Sultan Chand and
Sons
7 Rice A. John. Mathematical statistics and data Analysis (Third edition); Thomson
8 Goon Gupta Das Gupta; Fundamental of Statistics, Vol I & II, World press
Annexure ‘AAB-CD-01’
Course Title: Nonparametric Methods
Course Code: [STAT 905]
Credit Units: 4
Level: Doctoral (PhD)
#
L
T
3
1
Course Title
P/
S
SW/F
W
0
Weightage (%)
Nonparametric Methods
1
2
3
Course Objectives:
 The main objective of the course is to provide the detailed
knowledge of the order statistics, distribution of order statistics
and recurrence relations.
 To develop the knowledge of theory and applications of nonparametric methods.
Prerequisites:
NIL
Student Learning Outcomes:

The students will learn about the concepts and applications of
order statistics to handle the real life problems.

The students will able to learn how to solve the problems by
using non-parametric methods.

The students will learn about the various non-parametric tests.

4
5
6
7
8
The students will able to distinguish between one sample and
two sample non-parametric tests.
Module I: Order Statistics
Order statistics- their distributions and properties. Joint, marginal and
conditional distributions of order statistics. Censoring and progressive
censoring, order statistics for independent and non-identically distributed
variates. Expected values and moments of order statistics. Recurrence
relations and identities. Distribution free confidence intervals for quantiles
, Distribution free tolerance intervals, Order statistics as a Markov Chain.
Module II: Generalized order statistics
Generalized order statistics- distribution of generalized order statistics.
Joint, marginal and conditional distribution of generalized order statistics.
Moments and recurrence relations. Characterization of continuous
distributions through conditional moments and recurrence relations of
generalized order statistics. Review of latest literatures.
Module III: Non-parametric tests
Linear Rank Tests, Nonparametric Tests for Independence, Other
advanced nonparametric tests.
Module IV:
Nonparametric Density Estimation, Bootstrapping, Jackknifing.
Pedagogy for Course Delivery:
The class will be taught using theory and practical methods using
software in a separate Lab sessions. In addition to numerical applications,
the real life problems and situations will be assigned to the students and
they are encouraged to get a feasible solution that could deliver
meaningful and acceptable solutions by the end users. The focus will be
25
25
25
25
TOTAL
CREDIT
UNITS
4
9
given to incorporate the applications of order statistics and non-parametric
methods for solving the real life problems and cases.
Assessment/ Examination Scheme:
Theory L/T
(%)
Lab/Practical/Studio (%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Weightage
(%)
70%
End Term
Examination
MidTerm
Exam
HA
CP/
Viva
Attendance
10%
8%
7%
5%
70%
Text & References:
1.
2.
3.
4.
5.
6.
7.
8.
Gibbons, J.D. (1971): Non-parametric Statistical Inference, Mc Graw Hill Inc.Kamps, U. (1995): A
Concept of Generalized Order Statistics. B.G. Teubner Stuttgart
Makridakis, S., Wheelwright, S.C. and Hyndman, R.J. 1998. Forecasting: Methods and Applications.
John Wiley.
Pankratz, A. 1983. Forecasting with Univariate Box Jenkins Models: Concepts and Cases. John Wiley.
Hollander, M. and Wolfe, D.A. (1999). Nonparametric Statistical Methods. Wiley and Sons.
Gibbons, J.D. and Chakrabarty, S. (2010). Nonparametric Statistical Inference. Chapman and Hall/
CRC.
Arnold, B.C., Balakrishnan, N. and Nagaraja, H.N. (2008). A first course in order statistics. SIAM.
David, H. A. and Nagaraja, H.N. (2003). Order Statistics. Wiley and Sons.
Wassecman
Annexure ‘AAB-CD-01’
Course Title: Censoring Techniques in Biostatistics and Survival Analysis
Course Code: [STAT 903]
Credit Units: 4
Level: Doctoral (PhD)
#
L
T
3
1
P/
S
SW/F
W
Course Title:
Censoring Techniques in Biostatistics and Survival Analysis
1
Course Objectives:
1. To understand the basics and fundamentals theories and related
measurement in Biostatistics
2. To search for a feasible solution of real time problems of
Biostatistics, survival analysis and related applications.
3. To develop and promote research work in the field of Biostatistics
and its measurement using censoring techniques.
4. With the knowledge of the contents of the paper the students will
be able to apply Biostatistics fruitfully in industrial applications,
especially in medical sciences and related domain.
5. To resolve the issues related to model building using proportional
hazard function and estimation of survival function
6. To learn various theories, methods and applications to solve the
problem of competing risk using suitable statistical techniques.
To demonstrates the supporting statistical/stochastic/mathematical theory
through practical problems of day to day research activities in the field of
biostatistics and interdisciplinary applications
2
Prerequisites:
Graduate with mathematical statistics having knowledge of basic &
pure Statistics, Statistical modeling and probability theory & related
distributions, and elementary Biostatistics at PG level.
3
Student Learning Outcomes:
1. Develop and germinate research idea in biostatistics and
related domain.
2. The students will learn censoring techniques to deal with
applications in biostatistics and survival analysis.
3. The students will able to use different distributions for
0
TOTAL
CREDIT
UNITS
4
Weightage (%)
modeling the survival functions.
4. The students will able to construct proportional hazard
model.
5.
Inculcate problem solving ability among the students
related to Kaplan-Meier estimator and Nelson-Aalen
estimator
Course Contents / Syllabus:
4
Module I:
Introduction to censoring and truncation, difference in censoring and
truncation, right censoring, left censoring and interval censoring.
Likelihood construction for censored and truncated data, counting
processes, exercises, compliments and problems.
5
20%
Module II:
Non-parametric estimation of basic quantiles for right censored and 30%
left truncated data. Estimates of the survival and the cumulative
hazard function for right
censored data, point wise confidences
interval for the survival function, confidence bands for the survival
function. Point and interval estimates of the mean and median survival
time. Estimators of the survival function for left truncated and right
censored data compliments and problems
6
Module III:
Semi parametric proportional hazards regression with fixed covariates. 35%
Model building using the proportional hazards model, estimation of
survival function. Kaplan-Meier estimator and Nelson-Aalen
estimator. compliments and problems
7
Module IV:
Competing risks Analysis (parametric and nonparametric), Theory of
Dependent and Independent Risks. Complements and problems, case
discussion.
8
Pedagogy for Course Delivery:
1. All the topics covered in the syllabus will be correlated with its
applications in real life situations and also in other disciplines.
2. Extra sessions for revision will be undertaken.
3. Research focus should be given through out the modules.
4. Use of suitable software for computational purposes and
related solutions will be given priority in coverage of the
syllabus.
9
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
End Term
Examination
30%
NA
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Components
(Drop down)
Mid-
HA
CP/
Attendance
70%
End Term
Examination
15%
Term
Exam
Weightage
(%)
15%
Viva
8%
7%
5%
70%
Text & References:
1. Rupert G., Miller Jr.: Survival Analysis John. Wiley and Sons Ltd.
2. John P. K., Melvin L. Moeschberger: Survival Analysis Techniques for Cencored and
truncated Data Second edition, Springer.
3. David and Moeschberger: Competing Risk Theory Springer
4. Biswas, S.: Applied Stochastic Processes A Biostatistical and population Oriented
Approach. New central Book Agency PVT
5. Despande and Purohit, Lifetime data
6. Cox-Analysis of survival data
7. Crowder, M. competing Risks.
Annexure ‘AAB-CD-01’
Course Title: Reliability Theory and Methods
Course Code: STAT 904
Credit Units: 4
Level: Doctoral (PhD)
L
T
3
1
P/
S
SW/F
W
# Course Title: Reliability Theory and Methods
1 Course Objectives:
1. To understand the basics and fundamentals of reliability theory
and related measurement.
2. To handle and get a feasible solution to real time problems of
engineering Statistics and related applications.
3. To develop and promote research work in the field of
Reliability and its measurement.
4. With the knowledge of the contents of the paper the students
will be able to apply engineering statistics fruitfully in
industrial applications.
5. To resolve the issues related to system and component
reliability.
6. To learn various theories, methods and applications to solve
the problem of mechanical reliability using suitable statistical
techniques.
7. To
demonstrates
the
supporting
statistical/stochastic/mathematical theory through practical
problems of day to day research activities as well as
interdisciplinary applications.
2 Prerequisites:
Graduate with mathematical statistics having knowledge of basic
& pure Statistics, Statistical modeling and probability
distributions at PG level.
3 Student Learning Outcomes:
0
TOTAL
CREDIT
UNITS
4
Weightage (%)
1. Develop and germinate research idea.
2. The students will learn how to construct the systems for
getting the maximum reliability.
3. The students will able to use different distributions for the
study of systems.
4. The students will able to construct Life cycle curves.
5. Inculcate problem solving ability among the students
related to component and system reliability
Course Contents / Syllabus:
4 Module I:
Reliability, Importance of Reliability, Types of Reliability, Failures 20%
and Failure Modes. Causes of Failures. Failure Rate. Hazard Function.
Reliability in terms of Hazard Rate and Failure Density Functions.
Hazard Models: Constant Hazard Model, Linear and Non-Linear
Hazard Models, Weibull Model, Gamma Model and Normal Model.
Markov Model. Estimation of Reliability and Failure Density
Functions of Hazard and Markov Models. Mean Time to System
Failure (MTSF). Relation between MTSF and Reliability. Mean Time
Between Failures (MTBF).
5 Module II:
System and System Structures. Evaluation of Mean Time to System 30%
Failure (MTSF) and Reliability of The Systems: Series, Parallel,
Series-Parallel, Parallel-Series, Non-Series-Parallel, Mixed Mode and
k-out-of-n. Reliability Evaluation of Systems by Decomposition.
Coherent system and Preventive maintenance policy.
6 Module III:
Life cycle curves and probability distribution in modeling reliability, 15%
Reliability of the system with independent limit connected in (a)
Series (b) parallel and (c) K out of n system.
7 Module IV:
Evaluation of Reliability and Availability of Parallel-Unit System with 35%
Repair Using Markovian Approach. Reliability and Availability
Analysis of Single Unit, Two-Unit Cold Standby and Parallel-Unit
Systems with Constant Failure, Arbitrary Repair Rates and Waiting
Time of the Server Using semi-Markov Process and Regenerative
Point Technique. Supplementary Variable Technique.
8 Pedagogy for Course Delivery:
3. All the topics covered in the syllabus will be correlated with its
applications in real life situations and also in other disciplines.
4. Extra sessions for revision will be undertaken.
5. For computational aspects use of software v.i.z. R-GUI, SAS,
MS SOLVER, Minitab etc. will be used as per requirements
and suitability of the problems.
9
Assessment/ Examination Scheme:
Theory L/T (%)
Lab/Practical/Studio (%)
30%
Theory Assessment (L&T):
Continuous Assessment/Internal Assessment
Component
s (Drop
down)
Weightage
(%)
MidTerm
Test
HA
CP/
Viva
Attendanc
e
15%
8%
7%
5%
NA
End Term
Examinati
on
70%
Text & References:
1. Zacks: Introduction to reliability analysis, probability models and statistical, SpringerVerlag.
2. Biswas, S. (2007): Statistics of Quality control, Sampling Inspection and reliability,
New Central Book Agency.
3. Barlow, R.E. and Proschan, F. (1965) Mathematical Theory of Reliability, Wiley, New York,
NY.
4. Barlow, R.E. and Proschan, F. (1975) Statistical Theory of Reliability, Holt, Rinehart &
Winston, New York, NY.