FRIDAY, May 2, 2003
Time: 2:00 - 3:00 PM
Constant Hall Room 1052

Ph.D. Pre-defense
Title: Analysis of Multivariate Data Using Kotz Type Distribution

Kusaya Plungpongpun
Department of Mathematics & Statistics, Old Dominion University

In general, the tests available for multivariate normality are not very sensitive. Although in practice, most of the multivariate statistical inference is performed under the assumption of multivariate normality, we cannot guarantee that the data come from this distribution. It is therefore important to explore the use of other distributions for multivariate data analysis. In this talk we consider a probability distribution, called Kotz type distribution, which has fatter tail regions than that of multivariate normal distribution. We discuss various characteristics of this distribution, such as, its moments, the marginal, and conditional distributions. We also discuss how to simulate samples from this distribution. Estimation of parameters of this model using maximum likelihood method under a variety of covariance structures, such as, AR(1), equicorrelation and the unstructured covariance is also discussed. We show that the MLE of the location parameter under the assumption of Kotz type distribution is same as the generalized spatial median (GSM) defined by C. R. Rao (1988). We provide computational algorithm and computer programs to compute the estimates. Using the asymptotic distribution of the estimates we perform multivariate analysis of variance (MANOVA) under Kotz type distribution.