COURSES OF STUDIES STATISTICS HONOURS

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COURSES OF STUDIES for 2014-2015 (ADMISSION BATCH) BACHELOR OF ARTS

1 COURSES OF STUDIES for (ADMISSION BATCH) BACHELOR OF ARTS AND BACHELOR OF SCIENCE STATISTICS HONOURS RAVENSHAW UNIVERSITY CUTTACK

2 SEMESTER I BASIC MATHEMATICS PAPER 1 (AH ) and (SH ) F.M. : Unit 1 Linear Algebra Permutation and combinations, binomial theorem, vector spaces over real field, sub spaces, linear combination of vectors, examples in with geometrical interpretations, linear dependence and independence of vectors, dimension and basis of a vector space (elementary concepts and simple applications only). Matrices: types of matrices, singular and non-singular matrices, matrix operations, rank and inverse of a matrix. Determinants, characteristic equations and latent roots. Quadratic forms: positive definite forms and canonical form. Unit 2 Real Analysis Limits of sequence, convergence of infinite series, simple tests on convergence. Convergence of infinite and improper integrals, gamma integral, beta integral and their relationship. Unit 3 Calculus Limit and Continuity. Differentiation, differential coefficients from first principle, differential coefficients of sum, product and quotient, differential coefficient of a function. Definite integral, integration by substitution, integration by parts. 1. Apostol, T. M. (2007). Calculus Vol. 1, John Wiley & Sons. [Chapters 3, 4, 5 for Unit 3; Chapters 10 for Unit 2] 2. Santi Narayan: A Text Book of Matrices, S. Chand and Company Ltd. [Chapters 1, 2, 3, 4, 5, 8 & 11 for Unit 1]

3 1. Apostol, T. M.: Mathematical Analysis, Narosa Publishing House, New Delhi. 2. Santi Narayan: A Text Book of Calculus, S. Chand and Company Ltd. 3. Bartle, R. G. and D. R. Sherbert. (2011). Introduction to Real Analysis, Wiley. 4. Rao, A.R. and P. Bhimasankaram. (2000). Linear Algebra, Hindustan Book Agency, Delhi, India. 5. Rao, C. R. (2001). Linear Statistical Inference and its Applications, Wiley-Interscience. 6. Hadley, G. (1987). Linear Algebra, Narosa Publishing House, New Delhi. STATISTICAL METHODS & PROBABILITY PAPER 2 (AH ) and (SH ) Unit 1 Descriptive Statistics Measures of central tendency, measures of dispersion, moments, skewness and kurtosis and their measures, Sheppard s correction for grouped data (without proof). Unit 2 Probability I Terminology: trials, events, sample space, mutually exclusive events, exhaustive number of cases, independent events, equally likely cases, favourable number of cases. Definition of probability: classical, relative frequency and axiomatic approach, probability space, law of addition and law of multiplication of probability, conditional probability and independence of events, Baye s theorem and its applications. Unit 3 Probability II Random variables, probability mass function and probability density function.

4 Distribution function, joint, marginal and conditional distributions. Expectation of a random variable, addition and multiplication laws of expectation, moment and cumulant generating function. 1. Gupta, O.P. Mathematical Statistics, Kedarnath Ramnath and Co. 2. Gupta, S.C. and Kapoor V.K. Fundamentals of Mathematical Statistics, Sultan Chand and Sons. 3. Goon, A.N., Gupta, M.K. and Dasgupta, B. Fundamentals of Statistics Vol I, World Press. 1. David, S. Elementary Probability, Oxford Press.. 2. Rohatgi, V. K. and Md. E. Saleh. (2001). An introduction to probability and statistics, Wiley. 3. Mood, A.M., Graybill, F.A. and Boes, D.C. Introduction to theory of Statistics, McGraw Hill International Edition. PRACTICAL PAPER 3 (AH ) and (SH ) F.M. : Time 6 Hours 1. Measures of central tendency and dispersion, their computation and interpretation 2. Computation of first four moments for grouped and ungrouped data. 3. Calculation of skewness and kurtosis. SEMESTER II

5 STATISTICAL METHODS PAPER 4 (AH ) and (SH ) F.M. : Unit 1 Statistical Methods I Curve fitting by the method of least squares (polynomial, logarithmic and exponential), correlation and regression for grouped and ungrouped data, correlation ratio, intra class correlation, rank correlation. Unit 2 Statistical Methods - II Multiple regression, multiple and partial correlation (3 variables only). Unit 3 Statistical Methods - III Theory of attributes: consistency of data, independence and association of attributes, various measures of association. 1. Gupta, S.C. and V.K. Kapoor. Fundamentals of Mathematical Statistics, Sultan Chand and Sons.. 2. Gupta, O.P. Mathematical Statistics, Kedarnath Ramnath and Co. 3. Goon, A.N., M.K. Gupta and B. Dasgupta. Fundamentals of Statistics Vol I, World Press. 1. Bhat B.R, T. Srivenkatramana and Madhava. K.S. Rao. Statistics: A Beginner s Text, Vol. I, New Age International (P) Ltd. 2. Croxton F.E, D.J. Cowden and S. Kelin. Applied General Statistics, Prentice Hall of India. 3. Anderson T.W and S. L. Sclove. An Introduction to the Statistical Analysis of Data, Houghton Miffin Co.

6 4. Mood, A.M., F.A. Graybill and D.C. Boes. Introduction to theory of Statistics McGraw Hill International Edition PROBABILITY DISTRIBUTIONS PAPER 5 (AH ) and (SH ) F.M. : Unit 1 Discrete Probability Distributions Discreet uniform, Bernoulli, binomial, negative binomial and Poisson distributions. Their properties. Unit 2 Continuous Probability Distributions -I Rectangular, normal, gamma and beta distribution (1 st and 2 nd kind). Their properties. Unit 3 Continuous Probability Distributions II Exponential, Cauchy and bivariate normal distribution. Their properties. 1. Gupta, O.P. Mathematical Statistics, Kedarnath Ramnath and Co. 2. Gupta, S.C. and Kapoor, V.K. Fundamentals of Mathematical Statistics, Sultan Chand and Sons. 3. Mood, A.M., Graybill, F.A. and Boes, D.C. Introduction to theory of Statistics McGraw Hill International Edition. 1. Kotz, S., N. Balakrishnan and N. L. Johnson. (2005). Univariate Discrete Distributions 3rd Edition, John Wiley & Sons.

7 2. Kotz, S., N. Balakrishnan and N. L. Johnson. (2005). Continuous Univariate Distributions 2nd Edition, Volume 1, John Wiley & Sons. 3. Kotz, S., N. Balakrishnan and N. L. Johnson. (2005). Continuous Univariate Distributions 2nd Edition, Volume 2, John Wiley & Sons. 4. Feller, W. An Introduction to Probability Theory and Its Applications, Wiley. PRACTICAL PAPER 6 (AH ) and (SH ) F.M. : Time 6 Hours 1. Fitting of 1 st, 2 nd degree polynomials and exponential curves. 2. Computation of correlation coefficient for grouped and ungrouped data. 3. Computation of rank correlation coefficient (ties and without ties). 4. Obtaining regression coefficients and regression lines for grouped and ungrouped data. 5. Calculation of multiple and partial correlation and plane of regression (three variables). 6. Coefficient of association for attributes its computation and interpretation. 7. Fitting of Binomial, Poisson and Normal distributions. SEMESTER III OF ESTIMATION PAPER 7 (AH ) and ( SH ) F.M. : Unit 1 Characteristics of Estimators Estimators, properties of a good estimator, Cramer-Rao inequality and its applications.

8 Unit 2 Sufficiency Concept of sufficiency, Rao-Blackwell theorem and its applications, minimum variance unbiased estimator (MVUE), concept of complete sufficient statistic with illustration. Unit 3 Methods of Estimation Method of maximum likelihood and its properties, method of moments, method of minimum variance, interval estimation. 1. Gupta O.P. Mathematical Statistics, Kedarnath Ramnath and Co. 2. Gupta S.C. and Kapoor V.K. Fundamentals of Mathematical Statistics, Sultan Chand and Sons 1. Casella, G. and Roger L. Berger. (2001). Statistical Inference, Cengage Learning. 2. Hogg, R. V. and A. Craig. (1995). Introduction to Mathematical Statistics, Prentice Hall. 3. Lehmann, E.L. and C. George. (1998). Theory of Point Estimation, Springer. 4. Rao, C. R. (2001). Linear Statistical Inference and its Applications, Wiley-Interscience. TESTING of HYPOTHESIS PAPER 8 (AH ) and (SH ) Unit 1 Testing of Hypothesis

9 Concept of population, sample, parameter, null and alternative hypothesis, test of significance, one tailed and two tailed tests, type 1 and type 2 errors etc. sampling distribution of mean and variance from normal distribution, large sample theory and large sample tests. Unit 2 Exact Sampling Tests - 1 Chi-square distribution and its applications (test for homogeneity of population variance, test of goodness of fit and test of independence of attributes) Unit 3 Exact Sampling Tests - 2 Small sample theory, t and F distributions, applications of t and F distributions, Fisher s Z transformation, tests for sample correlation coefficient and regression coefficient (two variables only). 1. Gupta S.C. and Kapoor V.K. Fundamentals of Mathematical Statistics, Sultan Chand and Sons 2. Gupta O.P. Mathematical Statistics, Kedarnath Ramnath and Co. 1. Casella, G. and R. L. Berger. (2001). Statistical Inference, Cengage Learning. 2. Goon, A.N., M. K. Gupta and B. Dasgupta. Fundamentals of Statistics Vol I, World Press. 3. Rohatgi, V. K. and Md. E. Saleh. (2001). An Introduction to Probability and Statistics, Wiley. 4. Rao, C. R. (2001). Linear Statistical Inference and its Applications, Wiley-Interscience. PRACTICAL PAPER 9 (AH ) and (SH ) F.M. : Time 6 Hours

10 1. Tests based on Chi-square distribution. 2. Tests based on t distribution. 3. Tests based on F distribution. 4. Tests based on Fisher s Z transformation. 5. Record and Viva voce. SEMESTER IV PROBABILITY, TESTING of HYPOTHESIS and NON-PARAMETRIC METHODS PAPER 10 (AH ) and (SH ) UNIT 1 Testing of Hypothesis - 2 Meaning and concepts of tests, simple and composite hypothesis, power of tests, tests of simple hypothesis, most powerful tests, Neyman Pearson lemma and applications, uniformly most powerful tests, unbiased tests. Tests of composite hypothesis, likelihood ratio test and its applications. UNIT 2 Non-Parametric Tests Parametric versus non-parametric tests, advantages and disadvantages of non-parametric tests, sign test, run test, Mann Whitney U tests, Kolmogorov- Smirinov test, test of randomness, median test. UNIT 3 Probability Characteristic function, simple applications of Levy s inversion theorem (without proof), convergence in probability and convergence in distribution, Helly-Bray theorem, Levy-Cramer

11 theorem, ideas about weak laws and strong laws of large numbers, Chebychev s theorem, Khintchin s theorem, Bernoulli s theorem, central limit theorem ( Lindberg Levy form). 1. Gupta S.C. and Kapoor V.K. Fundamentals of Mathematical Statistics, Sultan Chand and Sons. 2. Gupta O.P. Mathematical Statistics, Kedarnath Ramnath and Co. 1. Casella, G. and Roger L. Berger. (2001). Statistical Inference, Cengage Learning. 2. Rohatgi, V. K. and Md. E. Saleh. (2001). An introduction to probability and statistics, Wiley. 3. Rao, C. R. (2001). Linear Statistical Inference and its Applications, Wiley-Interscience. 4. Lehmann, E.L. and J. P. Romano. (2010). Testing Statistical Hypotheses 3rd edition, Springer. NUMERICAL ANALYSIS and OPERATIONS RESEARCH PAPER 11 (AH ) and (SH ) F.M. : UNIT 1 Numerical Analysis Operators E and, factorial notations, separation of symbols, divided difference, interpolation with equal and unequal intervals, inverse interpolation, numerical integration. UNIT 2 Operations Research - 1

12 Linear Programming Problems (LPP): Application and limitations, formulation and solution of lpp by graphical method, solution of LPP by simplex method, use of artificial variables. UNIT 3 Operations Research 2 Game Theory, Duality, Transportation Problems, Assignment Problems. 1. Sastry, S.S. (2002). Introductory Methods of Numerical Analysis, Prentice Hall. 2. Taha, H.A. (2008). Operations Research: An Introduction, Pearson Education. 1. Gass, S.I. (2003). Linear Programming Methods and Applications, Courier Dover Publications. PRACTICAL PAPER 12 (AH ) and (SH ) F.M. : Time 6 Hours 1. Calculation of power of a test for testing the mean of a Normal distribution with known variance. 2. Applications of Sign test, Run test, Mann Whitney U tests, Kolmogorov - Smirinov test, Test of randomness, Median test. 3. Interpolation with equal and unequal intervals using Newton s formula and Lagrange s formula. 4. Numerical integration: Applications of Simpson s one third and three eights rule and Weddle s formula. 5. Formulation and Solution of LPP by Graphical Method. 6. Solution of LPP by Simplex Method. 7. Problems on Game theory. 8. Problems on Duality.

13 9. Transportation Problems and Assignment Problems. SEMESTER V DESIGN of SAMPLE SURVEYS PAPER 13 (AH ) and (SH ) F.M. : UNIT 1 Basic concepts, important steps in sample survey, principles of sample surveys, sampling and non-sampling errors, methods of drawing samples, types of sampling merits and limitations of sample surveys. UNIT 2 Simple random sampling with and without replacements, characteristics and methods of selection, estimation of population mean/total, standard error and its estimate, determination of sample size. UNIT 3 Stratified random sampling definition, method of selection, estimation of population mean/total with standard error and its estimate, problems of allocations: proportional and optimum, comparison with simple random sampling. Systematic sampling method of selection, estimation of population mean/total, sampling variance, comparison with simple random sampling and stratified sampling. 1. Gupta S.C. and V. K. Kapoor. Fundamentals of Applied Statistics, Sultan Chand and Sons.

14 2. Sukhatme, P.V. and B.V. Sukhatme: Sampling Theory of Surveys with Applications, Indian Soc. of Agric. Stat., New Delhi. 1. Cochran, W.G. Sampling Techniques Third edition. Wiley. 2. Des Raj and Chandok. Sampling design. Tata Mc Graw Hill. 3. Mukhopadhyay, P. Theory and Methods of Survey Sampling, Prentice Hall. 4. Goon, A.M., M. K. Gupta, B. Das Gupta. Fundamentals of Statistics, Vol. II, World Press, Calcutta. DESIGN of EXPERIMENTS PAPER 14 (AH ) and (SH ) UNIT 1 Linear models, tests of general linear hypothesis, analysis of variance (ANOVA) for one way and two way classified data (one observation per cell). Terminology and principles of design of experiment: replication, randomization and local control. UNIT 2 Complete Randomized Design (CRD), Randomized Block Design (RBD), Latin Square Design (LSD) and their relative efficiency. UNIT 3 Missing plot technique in RBD and LSD (one missing value), 2 2, 2 3 and 2 n factorial experiments. 1. Gupta S.C. and Kapoor V.K. Fundamentals of Applied Statistics, Sultan Chand and Sons.

15 2. Goon, A.M., M. K. Gupta, B. Das Gupta. Fundamentals of Statistics, Vol. II, World Press, Calcutta 3. Das, M.N. and Giri, N.C.: Designs of Experiments, Wiley Eastern. 1. Montgomery, D.C. Design and analysis of experiments. John Wiley. 2. Joshi, D.D. (1987). Linear Estimation and Design of Experiments, New Age International. DESIGN of SAMPLE SURVEYS PAPER 15 (AH ) and (SH ) UNIT 1 Unequal probability sampling with replacement probability proportional to size with replacement sampling, estimation of mean/total, method of selection, standard error of estimate and it s estimation, PPSWOR ( general selection procedure). UNIT-2 Use of auxiliary information in sample surveys, Ratio and Regression methods of estimation, Comparison of efficiency. UNIT-3 Cluster sampling equal and unequal size, estimation of population mean/total, standard error and its estimation, comparison with mean per unit estimator. Two-stage sampling with equal and unequal first stage units, estimation of population mean/total, standard error and its estimation, comparison with single-stage sampling.

16 1. Sukhatme, P.V. and Sukhatme, B.V.: Sampling Theory of Surveys with Applications, Indian Soc. of Agric. Stat., New Delhi. 2. Gupta S.C. and Kapoor V.K. Fundamentals of Applied Statistics, Sultan Chand and Sons. 1. Cochran, W.G. Sampling Techniques, Third edition, Wiley. 2. Des Raj and Chandok. Sampling design. Tata Mc Graw Hill. 3. Mukhopadhyay, P. Theory and Methods of Survey Sampling, Prentice Hall. 4. Goon, A.M., M. K. Gupta, B. Das Gupta. Fundamentals of Statistics, Vol. II, World Press, Calcutta. DESIGN of EXPERIMENTS PAPER 16 (AH ) and (SH ) UNIT-I Repeated Latin Squares, Greco L.S.D., orthogonal L.S.D., 3 2 Factorial experiments and their analysis. UNIT-2 Confounding: advantages and disadvantages, total and partial confounding in 2 2 and 2 3 factorial experiments. UNIT-III Split plot and Strip plot designs, balanced incomplete block designs. 1. Das, M.N. and Giri, N.C.: Designs of Experiments, Wiley Eastern.

17 2. Goon, A.M., M. K. Gupta, B. Das Gupta. Fundamentals of Statistics, Vol. II, World Press, Calcutta. 3. Gupta S.C. and Kapoor V.K. Fundamentals of Applied Statistics, Sultan Chand and Sons. 1. Kempthorne, O. The Design and Analysis of Experiments, Wiley. 2. Montgomery, D.C. Design and analysis of experiments. John Wiley. 3. Joshi, D.D. (1987). Linear Estimation and Design of Experiments, New Age International. PRACTICAL PAPER 17 (AH ) and (SH ) F.M. : Time 6 Hours 1. Analysis of CRD, RBD and LSD and comparison of efficiency. 2. Analysis of RBD and LSD with one missing value. 3. Analysis of 2 2, 2 3 and 2 4 factorial experiments. 4. Analysis of confounded 2 2, 2 3 and 2 4 ( total and partial) factorial experiments. 5. Analysis of split plot and strip plot designs, balanced incomplete block design. PRACTICAL PAPER 18 (AH ) and (SH ) Time 6 Hours 1. Drawing of simple random samples and estimation of population mean and total with standard errors. 2. Allocation of samples in stratified random sampling and estimation of population mean and total with standard errors. Comparison of efficiency with simple random sampling. 3. Drawing of systematic samples, comparison of efficiency with simple random sampling and stratified random sampling.

18 4. Drawing of PPS samples with replacement and estimation of population mean and total with standard errors. 5. Estimation of population mean and total with ratio and regression methods of estimation. Comparison of efficiency. SEMESTER VI TIME SERIES ANALYSIS PAPER 19 (AH ) and (SH ) UNIT-1 Definition and use, components of time series, measurement of trend: graphic method, method of semi average, method of moving average, method of least square. UNIT-2 Measurement of seasonal component: method of simple average, ratio to trend method, ratio to moving average method, link relative method. Measurement of cyclic component: simple method, method of harmonic analysis, periodogram analysis. UNIT-3 First and second order auto regressive series, autocorrelation and correlogram analysis. 1. Gupta, S.C. and Kapoor, V.K. Fundamentals of Applied Statistics, Sultan Chand and Sons. 2. Goon, A.M., M. K. Gupta, B. Das Gupta. Fundamentals of Statistics, Vol. II, World Press, Calcutta.

19 1. Chatfield, C. The Analysis of Time Series - An Introduction, Second edition, Chapman and Hall. 2. Anderson, T. W. The Statistical Analysis of Time Series, Wiley, N. Y. INDEX NUMBERS, OFFICIAL STATISTICS and STATISTICS in PSYCHOLOGY & EDUCATION PAPER 20 (AH ) and (SH ) UNIT-I Index Numbers: Definition, use and classification of Index Numbers, Important steps in construction of Index Numbers, Criteria of a good Index Number, Cost of Living Index Number and its construction and use, Base shifting, Splicing and Deflating of Index Numbers. UNIT-2 Official Statistics: Statistical organizations in Govt. of India and different states with reference to Odisha, Population Statistics, Agricultural Statistics, Industrial Statistics. UNIT-3 Psychological and Educational Statistics: Scaling procedure, scaling of rankings and ratings in terms of normal probability curve. Reliability of test scores, validity of test scores, Intelligence tests and Intelligence quotient. 1. Gupta, S.C. and Kapoor, V.K. Fundamentals of Applied Statistics, Sultan Chand and Sons. 2. Goon, A.M., Gupta, M.K. and B. Dasgupta. Fundamentals of Statistics, Vol. II, World Press.

20 1. Croxton, F.E. and D. J. Cowden. (1969). Applied General Statistics, Prentice Hall of India. INDUSTRIAL STATISTICS and COMPUTING PAPER 21 (AH ) and (SH ) UNIT-1 Industrial statistics statistical quality control, need for statistical quality control, control charts in general, random and assignable causes, purpose of control charts, process control, control charts for measurements, charts for averages, attributes, defectives and defects. UNIT-2 Acceptance sampling plans single and double sampling plans for attributes, producer s and consumer s risk, variable sampling plans, OC and ASN and ATI curves sequential sampling plans. Sequential sampling plan. UNIT-3 Understanding computers, parts of a computer, flow chart and algorithm. Statistical software for data analysis SPSS & R. Introduction to data base management systems, creating data base using common data base management systems. Introduction to common statistical softwares like SPSS and R. Importing data sets from data bases to SPSS and R. Books Recommended 1. Gupta, S.C. and Kapoor, V. K. Fundamentals of Applied Statistics, Sultan Chand and Sons. 2. Grant, E.L. and Leavenworth, R.S.: Statistical Quality Control, McGraw-Hill. 3. Sanders, H.D. Computer Today. References

21 1. Brownle e, K.A. Statistical Theory and Methodology in Science and Engineering, John Wiley and Sons. 2. Grant, E.L. Statistical Quality Control, McGraw Hill Wald, A.: Sequential Analysis, John Wiley. VITAL STATISTICS and DEMAND ANALYSIS PAPER 22 (AH ) and (SH ) UNIT-I Uses and sources of vital statistics, rates and ratios of vital events. measurement of mortality crude death rate, specific death rate, standardized death rate, infant mortality rate. Life tables: concept, assumption, construction and use, concept of stationary and stable population. UNIT-2 Abridged life tables: concept and construction. Measurement of fertility: crude birth rate, general fertility rate, specific fertility rate, total fertility rate, gross reproduction rate, net reproduction rate. UNIT-3 Demand Analysis: Law of demand, price determination in a competitive market, price-elasticity of demand, estimation of demand curve, determination of demand curve from market data, form of demand function, Engel s law and Engel s curve, income-elasticity of demand, different forms of Engel curve Books Recommended 1. Gupta S.C. and Kapoor V.K. Fundamentals of Applied Statistics, Sultan Chand and Sons.

22 2. Goon, A.M., Gupta, M.K. and B. Dasgupta. Fundamentals of Statistics, Vol. II, World Press. 1. Keyfitz, N. (1977). Applied Mathematical Demography, Springer Verlag. 2. Pathak, K. B. and F. Ram. (2011). Techniques of Demographic Analysis, Himalya Publishing House, Mumbai. PRACTICAL PAPER 23 (AH ) and (SH ) Time 6 Hours 1. Measurement of trend by graphic method, method of least square, method of moving average (Spencer s formula). 2. Measurement of Seasonal Component: Simple average method, Ratio to trend method, ratio to moving average method and link relative method. 3. Construction of index number by Laspeyre s method, Paasche s method and Fisher s method and tests for an ideal index number formula. 4. Construction of index number using price relatives. 5. Computation of mortality, fertility and reproduction rates. 6. Construction of complete and abridged life table. 7. Construction of control charts for mean, range, fraction defective and number of defectives. PROJECT PAPER 24 (AH ) and (SH ) F.M.: 30 (Project Report) + 20 (Presentation)

23 The students have to undertake a project under the guidance of a faculty member assigned by the Head of the Department. The project work should be chosen such that there is enough scope to apply and demonstrate the statistical techniques learnt in the honours program. The project report shall clearly state the problem addressed, the methodology adopted, the assumptions and hypotheses formulated, any previous references to the study undertaken, statistical analyses performed and the broad conclusion drawn.

SCHEME OF EXAMINATION

SCHEME OF EXAMINATION APPENDIX AE28 MANONMANIAM SUNDARANAR UNIVERSITY, TIRUNELVELI 12. DIRECTORATE OF DISTANCE AND CONTINUING EDUCATION POSTGRADUATE DIPLOMA IN STATISTICAL METHODS AND APPLICATIONS (Effective from the Academic