TUESDAY, July 8, 2003
Time: 2:00 - 4:00 PM
Constant Hall Room 1065

Ph.D. Defense
Title: Analysis of Multivariate Data Using Kotz Type Distribution

Kusaya Plungpongpun
Department of Mathematics & Statistics
Old Dominion University

Most of the inferential statistical methods for multivariate data are developed under the fundamental assumption that the data are from multivariate normal distribution. Unfortunately, one can never be sure whether a set of data is really from a multivariate normal distribution. There are numerous methods for checking (testing) multivariate normality, but based on many published and our own simulation studies, we observe that these tests are generally not very powerful, especially for smaller sample sizes. Hence it is always beneficial to have alternative multivariate distributions available along with the methodology for using them. In this talk we consider a probability distribution, called Kotz type distribution, which has fatter tail regions than that of multivariate normal distribution. We review some characteristics of this distribution, such as, its mean, variance, and Mardia's skewness and kurtosis measures. We also review estimation using maximum likelihood method under this distribution. An interesting and important observation is that the MLE of the location parameter is same as the generalized spatial median (GSM) defined by C. R. Rao (1988). Using the asymptotic distribution of the estimates we perform multivariate analysis of variance (MANOVA) under Kotz type distribution. Finally, discrimination and classification rules under Kotz type distribution are derived and compared with the rules based on multivariate normal distribution using estimated expected error of misclassification.