**DESCRIPTION OF COURSES**

**AS 562 ADVANCED STATISTICAL METHODS (2L+1P)**

*(Pre-requisite : AS 561)*

**Objective**

This course lays the foundation of probability distributions and sampling distributions and their application which forms the basis of Statistical Inference. Together with probability theory, this course is fundamental to the discipline of Statistics. The students are exposed to tests of significance, non-central distributions, order statistics. Categorical data analysis is also covered in this course.

**Theory**

UNIT I

Truncated and compound distributions. Fitting of orthogonal polynomials. Pearsonian curves. Categorical data analysis - loglinear models, Association between attributes. Variance stabilizing transformations.

UNIT II

Sampling distribution of correlation coefficient, regression coefficient, correlation ratio, intra class correlation coefficient.

UNIT III

Non-central t, χ2 and F distributions. Distribution of quadratic forms. Cochran’s theorem. Tests for normality. Large sample tests. Tests of significance based on t, χ2 and F distributions.

UNIT IV

Order statistics, distribution of rth order statistics, joint distribution of several order statistics and their functions, marginal distributions of order statistics, distribution of range, median etc.

**Practicals**

Fitting of truncated distribution, Fitting of Pearsonian curves, Analysis of association between attributes, categorical data. Fitting of non-central t, χ2 and F distributions. Computation of Tests of significance based on t, χ2 and F distributions. Order statistics.

**Suggested Readings**

- Agresti, A. 2002.
*Categorical Data Analysis*. John Wiley. - Arnold, B.C., Balakrishnan, N. and Nagaraja, H.N. 1992.
*A First Course in Order Statistics*. John Wiley. - David, H.A. and Nagaraja, H.N. 2003.
*Order Statistics*. John Wiley. - Dudewicz, E.J. and Mishra, S.N. 1988.
*Modern Mathematical Statistics*. John Wiley. - Goon, A.M. Gupta, M.K. and Dasgupta, B. 1986.
*Outline of Statistics.*Vol. I. World Press. - Goon, A.M., Gupta, M.K. and Dasgupta, B. 2008.
*Fundamentals of Statistics,*Vol. I. Atlantic Publishers. - Hoel, P.G. 1971.
*Introduction to Mathematical Statistics*. John Wiley. - Hogg, R.V. and Craig, T.T. 1995.
*Introduction to Mathematical Statistics*. Prentice-Hall. - Huber, P.J. 1981.
*Robust Statistics*. John Wiley. - Johnson, N.L., Kotz, S. and Balakrishnan, N. 2000.
*Discrete Univariate Distributions*. John Wiley. - Johnson, N.L., Kotz, S. and Balakrishnan, N. 2000.
*Continuous Univariate Distributions*. John Wiley. - Marek, F. 1963.
*Probability Theory and Mathematical Statistics*. John Wiley. - Mood, A. M. Graybill, F.A. and Boes, D.C. 1991.
*Introduction to Theory of Statistics*. Cambridge University Press. - Rao, C.R. 1965.
*Linear Statistical Inference and its Applications*. John Wiley. - Rohatgi, V.K. and Ehsan, M. 1991.
*Introduction to Probability Theory and Mathematical Statistics*. John Wiley. - Rohatgi, V.K. and Saleh, A.K. Md. E. 2005.
*An Introduction to Probability and Statistics*. John Wiley. - Searle, S. R. 1996.
*Linear Models*. Academic Press.