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Open AccessArticle

A Selective Overview of Skew-Elliptical and Related Distributions and of Their Applications

by Chris Adcock 1,† and Adelchi Azzalini 2,*,†
1
SOAS, University of London, London WC1H 0XG, UK
2
Dipartimento di Scienze Statistiche, Università di Padova, 35121 Padova, Italy
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2020, 12(1), 118; https://doi.org/10.3390/sym12010118
Received: 7 November 2019 / Revised: 29 December 2019 / Accepted: 2 January 2020 / Published: 7 January 2020
(This article belongs to the Special Issue Recent Advances on Symmetry in Mathematical Statistics)
Within the context of flexible parametric families of distributions, much work has been dedicated in recent years to the theme of skew-symmetric distributions, or symmetry-modulated distributions, as we prefer to call them. The present contribution constitutes a review of this area, with special emphasis on multivariate skew-elliptical families, which represent the subset with more immediate impact on applications. After providing background information of the distribution theory aspects, we focus on the aspects more relevant for applied work. The exposition is targeted to non-specialists in this domain, although some general knowledge of probability and multivariate statistics is assumed. Given this aim, the mathematical profile is kept to the minimum required. View Full-Text
Keywords: probability distributions; elliptical distributions; skew-elliptical distributions; flexible parametric distributions probability distributions; elliptical distributions; skew-elliptical distributions; flexible parametric distributions
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Adcock, C.; Azzalini, A. A Selective Overview of Skew-Elliptical and Related Distributions and of Their Applications. Symmetry 2020, 12, 118.

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