Flexible Modelling via Multivariate Skew Distributions

Abstract

Mixtures of skew component distributions are being applied widely to model and partition data into clusters that exhibit non-normal features such as asymmetry and tails heavier than the normal. The number of contributions on skew distributions are now so many that it is beyond the scope of this paper to include them all here. However, many of these developments can be considered as special cases of a (location-scale variant) of the fundamental skew normal (CFUSN) distribution or of the fundamental skew t (CFUST) distribution. We therefore focus on mixtures of CFUSN and CFUST distributions, along with a recently proposed extension that can be viewed as a scale-mixture of the CFUSN distribution, namely the canonical fundamental skew (symmetric generalized) hyperbolic (CFUSH) distribution.