Advanced Statistical Methods

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 also exposed to correlation and regression, and order statistics and their distributions. Categorical data analysis is also covered in this course.

 

  • Truncated and compound distributions. Fitting of orthogonal polynomials. Pearsonian curves. Categorical data analysis - Loglinear models, Association between attributes. Variance stabilizing transformations.
  • Sampling distribution of correlation coefficient, Regression coefficient, Correlation ratio, Intra class correlation coefficient.
  • 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.
  • 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.         

Fitting of truncated distribution: Fitting of Non-central t, χ2 and F distributions. Computation of Tests of significance based on t, χ2 and F distributions. Order statistics.