Statistics and Computing

, Volume 24, Issue 6, pp 971–984 | Cite as

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

  • Florence Forbes
  • Darren Wraith


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.


Covariance matrix decomposition EM algorithm Gaussian scale mixture Multivariate generalized t-distribution Outlier detection 

Supplementary material

11222_2013_9414_MOESM1_ESM.pdf (2.2 mb)
Missing Appendices, Tables, and Figures are available in a companion supplemental file. (PDF 2.2 MB)


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.INRIALaboratoire Jean Kuntzman, Mistis teamSaint-Ismier CedexFrance

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