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Date of Award

1995

Degree Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Supervisor

Dr. M.L. Tiku

Abstract

The assumption of normality appears prevalently in well-known statistical procedures. This may be a drawback, since it is very often the case that the data under study is not normally distributed. It is of interest to relax this normality assumption, and extend many commonly used statistical procedures to include non-normal situations.

With this in mind, we have proposed non-normal Regression and Analysis of Variance schemes based on Tiku and Suresh's (1992) Modified Maximum Likelihood procedure, for a symmetric non-normal family of distributions. The results have been derived both for complete and censored samples. The resulting non-normal procedures are exactly similar in form to the classical results, and are no more difficult to implement. They are also asymptotically fully efficient. Simulation studies have shown that the new methods are extremely efficient, even for distributions far from normal, and for small samples.

It is hoped that these new techniques present viable alternatives for data analysis when the normality assumption may not be justified.

Included in

Mathematics Commons

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