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**On mixtures of skew normal and skew \(t\)-distributions.**
*(English)*
Zbl 1273.62115

Summary: 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 data set, relative to other non-elliptically contoured clustering methods and associated algorithms for their implementation.

### MSC:

62H05 | Characterization and structure theory for multivariate probability distributions; copulas |

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

62H12 | Estimation in multivariate analysis |

65C60 | Computational problems in statistics (MSC2010) |

### Keywords:

skew symmetric distributions; multivariate skew normals; multivariate skew t-distributions; mixture models; maximum likelihood estimation; EM algorithm
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\textit{S. X. Lee} and \textit{G. J. McLachlan}, Adv. Data Anal. Classif., ADAC 7, No. 3, 241--266 (2013; Zbl 1273.62115)

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