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Flexible mixture modelling using the multivariate skew-t-normal distribution

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Abstract

This paper presents a robust probabilistic mixture model based on the multivariate skew-t-normal distribution, a skew extension of the multivariate Student’s t distribution with more powerful abilities in modelling data whose distribution seriously deviates from normality. The proposed model includes mixtures of normal, t and skew-normal distributions as special cases and provides a flexible alternative to recently proposed skew t mixtures. We develop two analytically tractable EM-type algorithms for computing maximum likelihood estimates of model parameters in which the skewness parameters and degrees of freedom are asymptotically uncorrelated. Standard errors for the parameter estimates can be obtained via a general information-based method. We also present a procedure of merging mixture components to automatically identify the number of clusters by fitting piecewise linear regression to the rescaled entropy plot. The effectiveness and performance of the proposed methodology are illustrated by two real-life examples.

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Acknowledgements

The authors are grateful to the Associate Editor and two anonymous referees for their insightful comments and valuable suggestions, which led to substantial improvements in the presentation of this work. This research was supported by the National Science Council of Taiwan (Grant no. NSC101-2118-M-005-006-MY2).

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Authors and Affiliations

  1. Institute of Statistics, National Chung Hsing University, Taichung, 402, Taiwan

    Tsung-I Lin, Hsiu J. Ho & Chia-Rong Lee

  2. Department of Public Health, China Medical University, Taichung, 404, Taiwan

    Tsung-I Lin

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  1. Tsung-I Lin
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Lin, TI., Ho, H.J. & Lee, CR. Flexible mixture modelling using the multivariate skew-t-normal distribution. Stat Comput 24, 531–546 (2014). https://doi.org/10.1007/s11222-013-9386-4

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