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Distributions generated by perturbation of symmetry with emphasis on a multivariate skew \(t\)-distribution. (English) Zbl 1065.62094
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.

MSC:
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H10 Multivariate distribution of statistics
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