amity university uttar pradesh · web viewmultivariate analysis is the analysis of observations on...

Annexure ‘AAB-CD-01’

Course Title: Advance Real AnalysisCourse Code: to be decided laterCredit Units: 4Level: PG

# Course Title Weightage (%)

1 Course Objectives: to understand the basic concepts of real analysis and its physical properties to develop fundamental knowledge and understanding of the many

techniques in Real variable . to make the students aware of General theory of differentiation and

integration under the sign of integration, question of convergence of series, Dirichlet’s integral, Laplace and Laplace Steiltjes transform are employed in the theory of probability distributions. Similarly, Bolzano-Weirstrass,Heine Borel theorems etc. are very much useful in Statistical Inference .

to apply statistical concepts to various fields of statistics to analyze and interpret data.

2 Prerequisites: NIL

3 Student Learning Outcomes:

The students will be able to learn various continuity of functions.

The students will able to acquire knowledge on convergences. The students will able to apply the properties of mgf and cf for

distributions. The students will able to define sequences of the functions. The course enables the students to develop the skill set to

solve the problems based on real life situation.Course Contents / Syllabus:4 Module I: 20%

WeightageMonotone 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: 20% Weightage

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 - Leibnitz rule, Integration under the sign of differentiation. Dirichlet integral.

6 Module III: 30% Weightage

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.

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7 Module IV: Applications of mgf and cf for continuous distributions

30% Weightage

Laplace and Laplace-Steiltjes transforms. Solutitions of linear differential.Properties of Laplace transforms, Transforms of derivatives, Transforms of integrals, Evalualtion of integrals using Laplace transform, convolution theorem, Applications to differential equations, simultaneous linear equations with constant coefficient, unit step functions and Periodic functions.

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.

9Assessment/ Examination Scheme:

Theory L/T (%)

Lab/Practical/Studio (%) End Term Examination

30% NA 70%Theory Assessment (L&T):

Continuous Assessment/Internal AssessmentEnd Term

ExaminationComponents (Drop down)

Mid-Term Exam

Project Viva

Attendance

Weightage (%) 10% 10% 5% 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.


Course Title: PROBABILITY THEORYCourse Code: to be decided laterCredit Units: 4Level: PG


1 Course Objectives: The objective of the course is to develop knowledge of the

fundamentals of the probability theory for determining the risk and assessing the various problems based on it.

The application of this theory in various decision making problems especially under uncertainties.



The students will be able to distinguish between probability models appropriate to different chance events and calculate probability according to these methods.

The students will learn to get the solution of the problems based on probability space and limit theorems.

The students will learn to get the solution of the problems based on random variables and distribution functions.

The students will learn to get the solution of the problems based on mgf and cf for discrete and continuous distributions.

The course enables the students to develop the skill set to apply probability theory in real life problems.

Course Contents / Syllabus:4 Module I: Probability Space and Limit Theorems 20%

WeightageProbability Space:

Definition of probability Some simple properties Discrete probability space Induced probability space Other measures-Complements and problems

Limit Theorems: Introduction Modes of conversion Weak law of large numbers Strong law of large numbers Limiting moment generating functions Central limit theorem

5 Module II: Random variables and Distribution Functions 20% Weightage

Random variables Functions of Random variables Probability density function Probability mass function Distribution function and its properties Representation of distribution as a mixture of distributions Compound, truncated and mixture distributions Decomposition of distribution functions Distribution functions of vector random variables Correspondence theorem Complements and problems

6 Module III: Applications of mgf and cf for discrete distributions 30% Weightage

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Mathematical expectation and moments Probability generating function (PGF) Moment generating function (MGF) Characteristic function (CF): Definition and simple properties Examples of discrete distributions: Degenerate, Uniform, Bernaulli,

Binomial, Poisson, Geometric, Negative Binomial and Hyper geometric distribution,

Convergence of distribution function. Complements and problems

7 Module IV: Applications of mgf and cf for continuous distributions 30% Weightage

MGF and CF for continuous r.v. Inversion theorem Examples of continuous distributions: Uniform, Normal,

Exponential, Gamma, Beta, Weibull, Pareto, Laplace, Lognormal, Logistic and Log-Logistic distribution.

Bochner’s theorem Complements and problems


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.

9Assessment/ Examination Scheme:

Theory L/T (%) Lab/Practical/Studio (%) End Term Examination



ExaminationComponents (Drop down) Mid-

Term Exam

Project Viva Attendance

Weightage (%) 10% 10% 5% 5% 70%

Text & References:

1. Bhat, B. R (1981): Modern Probability Theory, Wiley Eastern Ltd., New Delhi.2. Rohatgi, V. K. (1988): An Introduction to Probability and Mathematical Statistics, Wiley,

Eastern Limited.


Course Title: STATISTICAL METHODSCourse Code: to be decided laterCredit Units: 4Level: PG


1 Course Objectives: The main objective of the course is to provide the detailed

knowledge of the characterization of all the useful discrete, absolutely continuous and singular distributions.

Interrelations of various Statistical models producing different families require further investigations.

To develop the knowledge of order statistics and theory and applications of non-parametric methods.



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. The students will able to distinguish between one sample and two

sample non-parametric tests.Course Contents / Syllabus:4 Module I: Order Statistics 20%

Weightage

Definition and concept of Order Statistics Discrete & continuous Order Statistics Joint and marginal distribution of order statistics Distribution of range Distribution of censored sample Numeric examples and applications based on continuous

distributions. Complement and problems

5 Module II: Interval estimation and U-Statistics 20% Weightage

Confidence intervals for distribution Quantiles Tolerance limits for distributions Asymptotic distribution of function of sample moments U-Statistics, Transformation and Variance stabilizing results. Complement and problems

6 Module III: Non-parametric tests-I (based on location) 30% Weightage

One sample problem: Sign test, signed rank test, Kolmogrov-Smirnov test, Test of independence (run test).

Two sample problem: Wilcoxon-Mann-Whitney test, Median test, Kolmogrov-Smirnov test, run test.

Complement and problems7 Module IV: Non-parametric tests-II (based on scale) 30%

Weightage Ansari-Bradely test Mood test Kendall’s Tau test Test of randomness Consistency of tests and ARE

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Complements and problems8 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.

9 Assessment/ Examination Scheme:





Term Exam


Weightage (%) 10% 10% 5% 5% 70%

Text & References:1. Gibbons, J.D. (1971): Non-parametric Statistical Inference, Mc Graw Hill Inc.2. Hogg, R.V. & Raise, A.T. (1978): Introduction to mathematical satsitics, Macmillan Pub. Co.

Inc.


Course Title: Linear algebra and applicationCourse Code: to be decided laterCredit Units: 4Level: PG

# Course Title Feedback Rating(on scale of 6 points)

1 Course Objectives: The motivation of introducing Linear Algebra course in Statistics is mainly to evolve the basics of Algebra. 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.



The students will learn about the basic concepts of vector space, linear transformation.

The students will able to compute the rank of the given matrix, eignvalues.

The students will able to learn how to calculate Generalized Inverses of matrices.

The students will learn about the quadratic forms, quadratic and singular value decomposition.

Course Contents / Syllabus:4 Module I: 20%

WeightageExamples 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.


Linear Transformations and Matrices, Kernel, Image, and Isomorphism, change of bases, Similarity, Rank and Nullity.


Inner Product spaces, orthonormal sets and the Gram-Schmidt Process, the Method of Least Squares.Basic theory of Eigenvectors and Eigenvalues, algebraic and geometric multiplicity of eigen value, diagonalization of matrices, application to system of linear differential equations .Factorization of Matrices

7 Module IV: 30% Weightage

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, Quadractic 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.



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Weightage (%) 10% 10% 5% 5% 70%

Text & References:

Biswas, S. (1997): A Text Book of Matrix Algebra, 2nd Edition, New Age International Publishers. Golub, G.H. and Van Loan, C.F.(1989): Matrix Computations, 2nd edition, John Hopkins University Press,

Baltimore-London. Nashed, M.(1976): Generalized Inverses and Applications, Academic Press, New York. Rao, C.R.(1973): Linear Statistical Inferences and its Applications, 2nd edition, John Wiley and Sons. 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 ApplicationsCourse Code: to be decided laterCredit Units: 4Level: PG


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.



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.

The students will able to plan and schedule the network analysis.Course Contents / Syllabus:4 Module I: 20%

WeightageLinear Programming Problems (LPP)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 .


Transportation Problems (TP)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.


Integer Linear Programming ProblemsInteger Linear Programming Problems, Mixed Integer Linear Programming Problems, Cutting Plane Method, Branch and Bound Method.


Project schedulingNetwork representation of a Project Rules for construction of a Network. Use of Dummy activity. The critical Path method (CPM) for constructing the time schedule for the project. Float (or shack) of an activity and event. Programme Evolution and Review Technique (PERT). Probability considerations in PERT. Probability of meeting the scheduled time. PERT Calculation, Distinctions between CPM and PERT.

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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.






Term Exam


Weightage (%) 10% 10% 5% 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 – ICourse Code: to be decided laterCredit Units: 4Level: PG


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.



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. The students will able to distinguish the common elements of

inference procedures.Course Contents / Syllabus:4 Module I: 20%

WeightageCriterion of a good estimator- unbiasedness, consistency, efficiency and sufficiency. Minimal sufficient statistics. Exponential and Pitman family of distributions. Complete sufficient statistic, Rav-Blackwell theorem, Lehmann-Scheffe theorem, Cramer-Rao lower bound approach to obtain minimum variance unbiased estimator (mvue).


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.


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.


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

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sided null against one sided alternative hypothesis.







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Weightage (%) 10% 10% 5% 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.

Annexure ‘AAB-CD-01’Course Title: Advanced Sample Theory Course Code: to be decided laterCredit Units: 4Level: PG


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.



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.

The students will able to conceptualize, conduct, interpret the statistical analyses for the different population.


WeightageEstimation of population mean, total and proportion in SRS and Stratified sampling. Estimation of gain due to stratification. Ratio and regression methods of estimation. Unbiased ratio type estimators. Optimality of ratio estimate .Separate and combined ratio and regression estimates in stratified sampling and their comparison.


Cluster sampling: Estimation of population mean and their variances based on cluster of equal and unequal sizes. Variances in terms of intra-class correlation coefficient. Determination of optimum cluster size.Varying probability sampling: Probability proportional to size (pps) sampling with and without replacement and related estimators of finite population mean.


Two stage sampling: Estimation of population total and mean with equal and unequal first stage units. Variances and their estimation. Optimum sampling and sub-sampling fractions (for equal fsu’s only).Selection of fsu’s with varying probabilities and with replacement


Double Sampling: Need for double sampling. Double sampling for ratio and regression method of estimation. Double sampling for stratification. Sampling on two occasions.Sources of errors in surveys: Sampling and non-sampling errors. Various types of non –sampling errors and their sources .Estimation of mean and proportion in the presence of non-response. Optimum sampling fraction among non–respondents. Interpenetrating samples. Randomized response technique.

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Weightage (%) 10% 10% 5% 5% 70%

Text & References:1. Cockran, W.G., (1977): Sampling Techniques, 3rd edition, John Wiley.2. Des Raj and Chandak (1998): Sampling theory, Narosa.3. Murthy, M.N. (1977): Sampling theory and methods. Statistical Publishing Society, Calcutta.4. Sukhatme et al. (1984): Sampling theory of surveys with applications, Lowa state university press and

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

international publishers

Annexure ‘AAB-CD-01’Course Title: Linear Model and Regression AnalysisCourse Code: to be decided laterCredit Units: 4Level: PG


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.



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.


WeightageLinear Estimation: Gauss-Markov linear Models, Estimable functions, Error and Estimation Spaces, Best Linear Unbiased Estimator (BLUE), Least square estimator, Normal equations, Gauss-Markov theorem, generalized inverse of matrix and solution of Normal equations, variance and covariance of Least square estimators.


Test of Linear Hypothesis: One way and two way classifications. Fixed, random and mixed effect models (two way classifications only), variance components


Linear Regression: Bivariate, Multiple and polynomials regression and use of orthogonal polynomials. Residuals and their plots as tests for departure

from assumptions of fitness of the model normality, homogeneity of

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variance and detection of outlines. Remedies.


Non Linear Models: Multi-collinearity, Ridge regression and principal components regression, subset selection of explanatory variables, Mallon’s

Cp Statistics.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 (%)

30%Theory Assessment (L&T):

Continuous Assessment/Internal Assessment

Components (Drop down) Mid-Term Exam Project Viva

Weightage (%)10% 10% 5%

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, 3rd Ed. Wiley. 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: Experimental DesignCourse Code: to be decided laterCredit Units: 4Level: PG


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 forhomework assignments and the term project.



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.


WeightageAnalysis of Basic Design: Asymptotic relative efficiency, Missing plot technique, Analysis of covariance for CRD and RBD.


Factorial Experiments: 2n, 32 and 33 systems only. Complete and Partial Confounding. Factorial Replication in 2n systems.


Incomplete Block Design: Balanced Incomplete Block Design, Simple Lattice Design, Split-plot Design, Strip-plot Design.


Application Areas: Response surface areas. First and second order designs. Model validation and use of transformation. Analysis of series experiments, groups of experiment in time and space.

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

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the knowledge and applications of reliability theory in industrial applications and problems solving.


Theory L/T (%) Lab/Practical/Studio (%)



Components (Drop down) Mid-Term Exam Project VivaWeightage (%)

10% 10% 5%

Text & References:

1. Das, M.N. and Giri, N.C. (1979): Design and Analysis of Experiment, Wiley Eastern.2. Giro (1986): Analysis of Variance, South Asian Publishers.3. Day, Alok (1986): theory of Block Design, Wiley Eastern.

Annexure ‘AAB-CD-01’Course Title: Mathematical DemographyCourse Code: to be decided laterCredit Units: 4Level: PG


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.



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.


WeightageSources of Demographic data, Coverage and content errors in demographic data, Chandrasekharan—Deming formula to check completeness of registration data, adjustment of age data- use of Whipple, Myer and UN indices. population transition theory.


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


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.


Internal migration and its measurement, migration models, concept of international Migration, Nuptiality and its measurements. Competing risk Theory: Measurement of competing risks, Inter-relations of the death probabilities, Estimation of crude, net and partial crude probabilities of death.

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10% 10% 5%

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 BiostatisticsCourse Code: to be decided laterCredit Units: 4Level: PG


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.



The students will able to use the applications of statistics in clinical data.

The students will able to interpret the results of the given data with the help of different mathematical models.


WeightageParametric methods for comparing two survival distributions viz. L.R test, Cox’s F-test. P-value, Analysis of Epidemiologic and Clinical Data: Studying association between a disease and a characteristic: (a) Types of studies in Epidemiology and Clinical Research (i) Prospective study (ii) Retrospective study (iii) Cross-sectional data, (b) Dichotomous Response and Dichotomous Risk Factor: 2X2 Tables (c) Expressing relationship between a risk factor and a disease (d) Inference for relative risk and odds ratio for 2X2 table, Sensitivity, specificity and predictivities, Cox proportional hazard model.


Bivariate normal dependent risk model. Conditional death density functions. Stochastic epidemic models: Simple and general epidemic models (by use of random variable technique). Basic biological concepts in genetics, Mendels law, Hardy- Weinberg equilibirium, random mating, distribution of allele frequency (dominant/co-dominant cases), Approach to equilibirium


Analysis of Epidemiologic and Clinical Data: Studying association between a disease and a characteristic: (a) Types of studies in Epidemiology and Clinical Research (i) Prospective study (ii) Retrospective study (iii) Cross-sectional data, (b) Dichotomous Response and Dichotomous Risk Factor: 2X2 Tables (c) Expressing relationship between a risk factor and a disease (d) Inference for relative risk and odds ratio for 2X2 table, Sensitivity, specificity and predictivities,


for X-linked genes, natural selection, mutation, genetic drift, equilibirium when both naturalselection and mutation are operative, detection and estimation of linkage in

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heredity. Planning and design of clinical trials, Phase I, II, and III trials. Consideration in planning aclinical trial, designs for comparative trials. Sample size determination in fixed sample designs.








10% 10% 5%

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. 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: Advanced Statistical Inference – IICourse Code: to be decided laterCredit Units: 4Level: PG


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.



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.


WeightageStatistical decision problem: Decision problem and 2-person game, non-randonized, mixed and randomized decision rules, loss function, risk function, admissibility, Bayes rules, minimax rules, least favourable distributions, complete class and minimal complete class.


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..


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.


Bayesian interval estimation, Bayesian testing of hypothesis, Bayes factor for various types of testing hypothesis problem depending upon whether the null hypothesis and the alternative hypothesis are simple or composite, Bayesian prediction problem.


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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


Course Title: Multivariate AnalysisCourse Code: to be decided laterCredit Units: 4Level: PG


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.



The students will learn various statistical techniques for multivariate data.

The students will able to do analysis by using different procedures for multivariate data.


WeightageSingular and non-singular multivariate normal distributions, Characteristic

function of N p ( μ ,∑ ) Maximum likelihood estimators of μ and ∑ ¿ ¿ in N p ( μ ,∑ ) and their independence.


Wishart distribution: Definition and its distribution, properties and characteristic function. Generalized variance. Testing of sets of variates and equality of covariance. Estimation of multiple and partial correlation coefficients and their null distribution, Test of hypothesis on multiple and partial correlation coefficients.


Hotelling’s T 2: Definition, distribution and its optimum properties. Application in tests on mean vector for one and more multivariate normal population and also on equality of the components of a mean vector of a multivariate normal population. Distribution of Mahalanobis’s D2. Discriminate analysis: Classification of observations into one or two or more groups. Estimation of the misclassification probabilities. Test associated with discriminate functions.


Principal component, canonical variate and canonical correlation: Definition, use, estimation and computation. Cluster analysis.


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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.

.

Annexure ‘AAB-CD-01’Course Title: Stochastic Processes and ApplicationsCourse Code: to be decided later L T P/

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TOTAL CREDIT UNITS

2 1 0 3

Credit Units: 3Level: PG


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.



The students will able to learn the basics of stochastic processes. The students will learn about the Renewal theory.


WeightageIntroduction to Stochastic Processes (sp’s); classification of sp’s according to state space and time domain. Countable state Markov chains (MC’s), Chapman-Kolmogorov 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.


Discrete state space continuous time MC, Kolmogorov- Feller differential equations, Poisson process, birth and death process


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.


Martingale in discrete time, inequality, convergence and smoothing properties, Queueing processes, application to queues –M/M/1 and M/M/C models.






http://en.wikipedia.org/wiki/Random_walk

http://en.wikipedia.org/wiki/Brownian_motion

http://en.wikipedia.org/wiki/Temperature

http://en.wikipedia.org/wiki/Blood_pressure

http://en.wikipedia.org/wiki/Electroencephalography

http://en.wikipedia.org/wiki/Electrocardiogram

http://en.wikipedia.org/wiki/Medicine

http://en.wikipedia.org/wiki/Video

http://en.wikipedia.org/wiki/Sound

http://en.wikipedia.org/wiki/Speech_communication

http://en.wikipedia.org/wiki/Exchange_rate

http://en.wikipedia.org/wiki/Stock_market

http://en.wikipedia.org/wiki/Random_variable

http://en.wikipedia.org/wiki/Random_variable


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Text & References:

Mehdi, 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 ControlCourse Code: to be decided later L T P/

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TOTAL CREDIT UNITS

2 1 0 3

Credit Units: 3Level: PG


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.



The students will learn the basic concepts of quality control for industrial purposes.

The students will able to construct various control charts for monitoring the process control.


WeightageBasic concept of process, monitoring and control process capability and process optimization, General theory and review of control charts for attribute and variable data; OC and A. R. L. of control charts, moving average and exponentially distributed moving average charts. Cu-Sum charts, using V-marks and decision interval.


Acceptance sampling plans for attribute inspection; single, double sampling plans and their properties, (ATI, AOQ, ASN,---------


Capability indices Cp, Cpk, and Cpm; estimation, confidence intervals and tests of hypothesis relating to capability for normally distributed characteristics.


Use of Design of Experiments in SPC; factorial experiments construction of such designs and analysis of data.






Continuous Assessment/Internal Assessment End Term Examination

Components (Drop down) Mid-

Term Exam


Weightage (%) 10% 10% 5% 5% 70%

Text & References:1. Montgomery, D. C. (1985): Introduction of Statistical Quality Control, Wiley.2. Montgomery, D. C. (1985): Design and Analysis of Experiments; Wiley.3. Ott, E. R. (1975): Process Quality Control. McGraw Hill.


Course Title: Survival AnalysisCourse Code: to be decided laterCredit Units: 3Level: PG


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).



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.Course Contents / Syllabus:4 Module I: 20%

WeightageConcepts of Type-I (time), Type-II (order) and random censoring likelihood in these cases. Lifedistributions, exponential, gamma, Weibull, lognormal, Pareto, linear failure rate. Inference forexponential, gamma, Weibull distributions under censoring.


Failure rate, mean residual life and their elementary properties. Ageing classes and their properties,bathtub failure rate.


Estimation of survival function – Actuarial estimator, Kaplan –Meier estimator, Tests of exponentiality against non-parametric classes: Total time on Test, Deshpande Test.


Two sample problem : Gehan test, Log rank test. Mantel-Haenszel test, Cox’s proportional hazards model, competing risks model.




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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 EconometricsCourse Code: to be decided laterCredit Units: 3

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Level: PG


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.



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 Market Equilibrium.


WeightageIntroduction to Mathematical EconomicsMathematical Economics: Meaning and Importance- Mathematical Representation of Economic Models- Economic functions: Demand function, Supply function, Utility function, Consumption function, Production function, Cost function, Revenue function, Profit function, Saving function, Investment function Marginal Concepts: Marginal utility, Marginal propensity to Consume, Marginal propensity to Save, Marginal product, Marginal Cost, Marginal Revenue, Marginal Rate of Substitution, Marginal Rate of Technical Substitution Relationship between Average Revenue and Marginal Revenue- Relationship between Average Cost and Marginal Cost - Elasticity: Demand elasticity, Supply elasticity, Price elasticity, Income elasticity, Cross elasticity- Engel function.


Constraint Optimisation, Production Function and Linear ProgrammingConstraint optimisation Methods: Substitution and Lagrange Methods-Economic applications: Utility Maximisation, Cost Minimisation, Profit Maximisation. Production Functions: Linear, Homogeneous, and Fixed production Functions- Cobb Douglas production function- Linear programming: Meaning, Formulation and Graphic Solution.


Market EquilibriumMarket Equilibrium: Perfect Competition- Monopoly- Discriminating Monopoly Nature and Scope of EconometricsEconometrics: Meaning, Scope, and Limitations - Methodology of econometrics - Types of data: Time series, Cross section and panel data.


The Linear Regression Model

Origin and Modern interpretation- Significance of Stochastic Disturbance term- Population Regression Function and Sample Regression Function-Assumptions of Classical Linear regression model-Estimation of linear Regression Model: Method of Ordinary Least Squares (OLS)- Test of Significance of Regression coefficients : t test- Coefficient of Determination.







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Text & References: Chiang A.C. and K. Wainwright, Fundamental Methods of Mathematical Economics, 4 th Edition, McGraw-

Hill, New York, 2005. (cw) 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. Johnsonton J,- Econometric methods–McGraw Hill Company,NewYork Croxton F.E and Cowden D.J-Applied General Statistics-Prentice Hall of India Pvt Ltd. Henderson and Quandt, Microeconomic Theory, McGraw Hill Company,NewYork.

Annexure ‘AAB-CD-01’Course Title: Modeling and SimulationCourse Code: to be decided laterCredit Units: 4Level: PG

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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.



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.


WeightageMathematical Model, types of Mathematical models and properties, Procedure of modeling, Graphical method: Barterning model, Basic optimization, Basic probability: Monte-Carlo simulation


Approaches to differential equation: Heun method, Local stability theory: Bernoulli Trials, Classical and continuous models, Case studies in problems of engineering and biological sciences.


General techniques for simulating continuous random variables, simulation from Normal and Gamma distributions, simulation from discrete probability dstributions, simulating a non – homogeneous Poisson Process and queuing system.







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Text & References: Edward A. Bender. An Introduction to Mathematical Modeling.

A. C. Fowler. Mathematical Models in Applied Sciences, Cambridge University Press. 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: Statistical GeneticsCourse Code: to be decided laterCredit Units: 4Level: PG

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3 1 0 4


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.



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.


WeightageFunctions 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).


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).


Basic biological concepts in genetics, Mendels law, Hardy- Weinberg equilibirium, random mating, distribution of allele frequency ( dominant/co-dominant 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.


Planning and design of clinical trials, Phase I, II, and III trials. Consideration in planning a clinical trial, designs for comparative trials. Sample size determination in fixed sample designs.







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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: Reliability Theory and ApplicationsCourse Code: to be decided laterCredit Units: 4Level: PG

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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.

2 Prerequisites:

NIL3 Student Learning Outcomes:

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.Course Contents / Syllabus:4 Module I: 20%

WeightageDefinition 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


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.


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)].


Accelerated testing, types of acceleration and stress loading. Life stress relationships. Arrhenius –lognormal, Arrhenius-Weibull, Arrhenius-exponential models, Power-Weibull and Power-exponential models







Term Exam


Weightage (%) 10% 10% 5% 5% 70%

Text & References:

1. Sinha,S.K. (1980): Reliability and life testing, Wiley,Eastern Ltd.2. Nelson, W. (1989): Accelerated Testing, Wiley.3. Zacks: Introduction to reliability analysis, probability models and statistical, Springer-Verlag.

Annexure ‘AAB-CD-01’Course Title: ACTUARIAL STATISTICSCourse Code: to be decided laterCredit Units: 4Level: PG


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.



The students will acquire the knowledge on various statistical techniques in insuarance field.

The students will able to compute risks for the given real life situation.

The students will learn about the Life annuities.Course Contents / Syllabus:4 Module I: 20%

WeightageUtility theory, insurance and utility theory, models for individual claims and their sums, survival function, curtate future lifetime, force of mortality. Life table and its relation with survival function, examples. Multiple life functions, joint life and last survivor status.


Multiple decrement models, deterministic and random survivorship groups, associated single decrement tables, central rates of multiple decrement. Distribution of aggregate claims, compound Poisson distribution and its applications. Claim Amount distributions, approximating the individual model, Stop-loss insurance.


Principles of compound interest: Nominal and effective rates of interest and discount, force of interestand 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.


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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.LabProblems based on All papers of Semester IV







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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 Acturila, 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.

amity university uttar pradesh · web viewmultivariate analysis is the analysis of observations on...

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