Stochastic representations and probabilistic characteristics of multivariate skew-elliptical distributions

TL;DR

This paper explores the properties and stochastic representations of multivariate skew-elliptical distributions, extending known properties of skew-normal distributions to a broader class and analyzing their probabilistic characteristics.

Contribution

It introduces stochastic representations for a general class of skew-elliptical distributions and investigates their key probabilistic properties.

Findings

Established stochastic representations for skew-elliptical distributions

Analyzed characteristic functions and moments of these distributions

Explored transformation properties and quadratic forms

Abstract

The family of multivariate skew-normal distributions has many interesting properties. It is shown here that these hold for a general class of skew-elliptical distributions. For this class, several stochastic representations are established and then their probabilistic properties, such as characteristic function, moments, quadratic forms as well as transformation properties, are investigated.