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Robust mixture modelling using skewed multivariate distributions with variable amounts of tailweight

Florence Forbes 1 Darren Wraith 1
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann
Abstract : The family of location and scale mixtures of Gaussians has the ability to generate a number of flexible distributional forms. It nests as particular cases several important asymmetric distributions like the Generalised Hyperbolic distribution. The Generalised Hyperbolic distribution in turn nests many other well-known distributions such as the Normal Inverse Gaussian (NIG) whose practical relevance has been widely documented in the literature. In a multivariate setting, we propose to extend the standard location and scale mixture concept into a so called multiple scaled framework which has the advantage of allowing different tail and skewness behaviours in each dimension of the variable space with arbitrary correlation between dimensions. Estimation of the parameters is provided via an EM algorithm with a particular focus on NIG distributions. Inference is then 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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https://hal.archives-ouvertes.fr/hal-02423639
Contributor : Florence Forbes <>
Submitted on : Tuesday, December 24, 2019 - 7:44:30 PM
Last modification on : Friday, December 4, 2020 - 9:56:37 AM

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Florence Forbes, Darren Wraith. Robust mixture modelling using skewed multivariate distributions with variable amounts of tailweight. JdS 2019 - 51èmes Journées de Statistique, Jun 2019, Nancy, France. ⟨hal-02423639⟩

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