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Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution

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  • Adelchi Azzalini
  • Antonella Capitanio

Abstract

Summary. A fairly general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non‐symmetric densities. The approach is sufficiently general to encompass some recent proposals in the literature, variously related to the skew normal distribution. The special case of skew elliptical densities is examined in detail, establishing connections with existing similar work. The final part of the paper specializes further to a form of multivariate skew t‐density. Likelihood inference for this distribution is examined, and it is illustrated with numerical examples.

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  • Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
  • Handle: RePEc:bla:jorssb:v:65:y:2003:i:2:p:367-389
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    File URL: https://doi.org/10.1111/1467-9868.00391
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    1. Marc Genton & Nicola Loperfido, 2005. "Generalized skew-elliptical distributions and their quadratic forms," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(2), pages 389-401, June.
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