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Advances in Data Analysis and Classification
Published in: Advances in Data Analysis and Classification 3/2013

01-09-2013 | Regular Article

On mixtures of skew normal and skew \(t\)-distributions

Authors: Sharon X. Lee, Geoffrey J. McLachlan

Published in: Advances in Data Analysis and Classification | Issue 3/2013

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Abstract

Finite mixtures 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 connection 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 symmetric distributions into four types, thereby clarifying their close relationships. This also aids in understanding the link between some of the proposed expectation-maximization 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.
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Metadata
Title
On mixtures of skew normal and skew -distributions
Authors
Sharon X. Lee
Geoffrey J. McLachlan
Publication date
01-09-2013
Publisher
Springer Berlin Heidelberg
Published in
Advances in Data Analysis and Classification / Issue 3/2013
Print ISSN: 1862-5347
Electronic ISSN: 1862-5355
DOI
https://doi.org/10.1007/s11634-013-0132-8

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