On Mixtures of Skew Normal and Skew t-Distributions

TL;DR

This paper systematically classifies mixtures of skew distributions, clarifies their relationships, compares EM-based estimation algorithms, and demonstrates their effectiveness in clustering real data.

Contribution

It provides a systematic classification of skew mixture models, clarifies their relationships, and evaluates their clustering performance on real data.

Findings

Skew mixture models effectively cluster heterogeneous data.

Classification clarifies relationships between different skew distributions.

Performance comparison shows advantages over other clustering methods.

Abstract

Finite mixture of skew distributions have emerged as an effective tool in modelling heterogeneous data with asymmetric features. With various proposals appearing rapidly in the recent years, which are similar but not identical, the connections between them and their relative performance becomes rather unclear. This paper aims to provide a concise overview of these developments by presenting a systematic classification of the existing skew distributions into four types, thereby clarifying their close relationships. This also aids in understanding the link between some of the proposed expectation-maximization (EM) based algorithms for the computation of the maximum likelihood estimates of the parameters of the models. The final part of this paper presents an illustration of the performance of these mixture models in clustering a real dataset, relative to other non-elliptically contoured clustering methods and associated algorithms for their implementation.