Finite mixture of skew distributions have emerged as an effective tool inmodelling heterogeneous data with asymmetric features. With various proposalsappearing rapidly in the recent years, which are similar but not identical, theconnections between them and their relative performance becomes rather unclear.This paper aims to provide a concise overview of these developments bypresenting a systematic classification of the existing skew distributions intofour types, thereby clarifying their close relationships. This also aids inunderstanding the link between some of the proposed expectation-maximization(EM) based algorithms for the computation of the maximum likelihood estimatesof the parameters of the models. The final part of this paper presents anillustration of the performance of these mixture models in clustering a realdataset, relative to other non-elliptically contoured clustering methods andassociated algorithms for their implementation.
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