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A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweight: application to robust clustering. (English) Zbl 1332.62204
Summary: 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 \(t\) tails. For these latter cases, we provide maximum likelihood estimation of the parameters and illustrate their modelling flexibility on simulated and real data clustering examples.

MSC:
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62H05 Characterization and structure theory for multivariate probability distributions; copulas
60E05 Probability distributions: general theory
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