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

Darren Wraith 1 Florence Forbes 1
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
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 Generalised Hyper-bolic distribution. The Generalised Hyperbolic distribution in turn nests many other well known distributions such as the Normal Inverse Gaussian. In a multi-variate 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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Darren Wraith, Florence Forbes. Location and scale mixtures of Gaussians with flexible tail behaviour: properties, inference and application to multivariate clustering. Computational Statistics and Data Analysis, Elsevier, 2015, 90, pp.61-73. ⟨10.1016/j.csda.2015.04.008⟩. ⟨hal-01970565⟩

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