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Location and scale mixtures of Gaussians with flexible tail behaviour: Properties, inference and application to multivariate clustering

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  • Wraith, Darren
  • Forbes, Florence

Abstract

The family of location and scale mixtures of Gaussians has the ability to generate a number of flexible distributional forms. The family nests as particular cases several important asymmetric distributions like the Generalized Hyperbolic distribution. The Generalized Hyperbolic distribution in turn nests many other well known distributions such as the Normal Inverse Gaussian. In a multivariate setting, an extension of the standard location and scale mixture concept is proposed into a so called multiple scaled framework which has the advantage of allowing different tail and skewness behaviours in each dimension with arbitrary correlation between dimensions. Estimation of the parameters is provided via an EM algorithm and extended to cover the case of mixtures of such multiple scaled distributions for application to clustering. Assessments on simulated and real data confirm the gain in degrees of freedom and flexibility in modelling data of varying tail behaviour and directional shape.

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  • Wraith, Darren & Forbes, Florence, 2015. "Location and scale mixtures of Gaussians with flexible tail behaviour: Properties, inference and application to multivariate clustering," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 61-73.
    • Handle: RePEc:eee:csdana:v:90:y:2015:i:c:p:61-73
    DOI: 10.1016/j.csda.2015.04.008
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    Cited by:

    1. Mohsen Maleki & Darren Wraith & Reinaldo B. Arellano-Valle, 2019. "A flexible class of parametric distributions for Bayesian linear mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 543-564, June.
    2. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2017. "A mixture of SDB skew-t factor analyzers," Econometrics and Statistics, Elsevier, vol. 3(C), pages 160-168.
    3. Sladana Babic & Laetitia Gelbgras & Marc Hallin & Christophe Ley, 2019. "Optimal tests for elliptical symmetry: specified and unspecified location," Working Papers ECARES 2019-26, ULB -- Universite Libre de Bruxelles.
    4. Loperfido, Nicola, 2024. "The skewness of mean–variance normal mixtures," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    5. Lee, Sharon X. & McLachlan, Geoffrey J., 2022. "An overview of skew distributions in model-based clustering," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    6. Perthame, Emeline & Forbes, Florence & Deleforge, Antoine, 2018. "Inverse regression approach to robust nonlinear high-to-low dimensional mapping," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 1-14.
    7. Lorenzo Ricci & David Veredas, 2012. "TailCoR," Working Papers 1227, Banco de España.
      • Sla{dj}ana Babi'c & Christophe Ley & Lorenzo Ricci & David Veredas, 2020. "TailCoR," Papers 2011.14817, arXiv.org.
    8. Eckhard Liebscher & Wolf-Dieter Richter, 2016. "Estimation of Star-Shaped Distributions," Risks, MDPI, vol. 4(4), pages 1-37, November.
    9. Mondal, Sagnik & Genton, Marc G., 2024. "A multivariate skew-normal-Tukey-h distribution," Journal of Multivariate Analysis, Elsevier, vol. 200(C).
    10. Tortora, Cristina & Franczak, Brian C. & Bagnato, Luca & Punzo, Antonio, 2024. "A Laplace-based model with flexible tail behavior," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).

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