DESCRIPTION OF COURSES

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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