Statistical applications of the multivariate skew-normal distribution

TL;DR

This paper explores the properties and statistical applications of the multivariate skew-normal distribution, extending its theoretical understanding and demonstrating its use in multivariate statistical problems with numerical examples.

Contribution

It provides new probabilistic insights and extends the distribution by introducing a skewing factor for elliptical densities, enhancing its applicability.

Findings

Enhanced understanding of probabilistic properties

Application to multivariate statistical problems

Introduction of a skewing factor for elliptical densities

Abstract

Azzalini & Dalla Valle (1996) have recently discussed the multivariate skew-normal distribution which extends the class of normal distributions by the addition of a shape parameter. The first part of the present paper examines further probabilistic properties of the distribution, with special emphasis on aspects of statistical relevance. Inferential and other statistical issues are discussed in the following part, with applications to some multivariate statistics problems, illustrated by numerical examples. Finally, a further extension is described which introduces a skewing factor of an elliptical density.