A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweights: Application to robust clustering

Florence Forbes 1 Darren Wraith 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 : We propose a family of multivariate heavy-tailed distributions that allow variable marginal amounts of tailweight. The originality comes from introducing multidimensional instead of univariate scale variables for the mixture of scaled Gaussian family of distributions. In contrast to most existing approaches, the derived distributions can account for a variety of shapes and have a simple tractable form with a closed-form probability density function whatever the dimension. We examine a number of properties of these distributions and illustrate them in the particular case of Pearson type VII and ttails. For these latter cases, we provide maximum likelihood estimation of the parameters and illustrate their modelling flexibility on simulated and real data clustering example.
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Florence Forbes, Darren Wraith. A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweights: Application to robust clustering. Statistics and Computing, Springer Verlag (Germany), 2014, 24 (6), pp.971-984. ⟨10.1007/s11222-013-9414-4⟩. ⟨hal-00823451v2⟩

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