  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.
