Distributions generated by perturbation of symmetry with emphasis on a multivariate skew $t$ distribution

TL;DR

This paper introduces a general method to generate non-symmetric multivariate densities by perturbing symmetric ones, focusing on skew elliptical and skew t distributions, and explores their properties and inference methods.

Contribution

It presents a unified approach to perturb multivariate symmetric densities, including skew t distributions, connecting various existing models and providing inference techniques.

Findings

Established connections with existing skew elliptical models

Developed likelihood inference methods for skew t distributions

Illustrated the approach with numerical examples

Abstract

A fairly general procedure is studied to perturbate a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is general enough to encompass a number of recent proposals in the literature, variously related to the skew normal distribution. The special case of skew elliptical densities is examined in detail, establishing connections with existing similar work. The final part of the paper specializes further to a form of multivariate skew $t$ density. Likelihood inference for this distribution is examined, and it is illustrated with numerical examples.