Introduction

Abstract

The multivariate normal distribution is undoubtedly one of the most well-known and useful distributions in statistics, playing a predominant role in many areas of applications. In multivariate analysis, for example, most of the existing inference procedures for analyzing vector-valued data have been developed under the assumption of normality. In linear model problems, such as the analysis of variance and regression analysis, the error vector is often assumed to be normally distributed so that statistical analysis can be performed using distributions derived from the normal distribution. In addition to appearing in these areas, the multivariate normal distribution also appears in multiple comparisons, in the studies of dependence of random variables, and in many other related areas.