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

Adcock, Chris; Azzalini, Adelchi

Abstract

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.

Citation

Adcock, C., & Azzalini, A. (2020). A Selective Overview of Skew-Elliptical and Related Distributions and of Their Applications. Symmetry, 12(1), 118. https://doi.org/10.3390/sym12010118

• Journal Article Type: Article
• Acceptance Date: Jan 2, 2020
• Online Publication Date: Jan 7, 2020
• Publication Date: Jan 7, 2020
• Deposit Date: Mar 3, 2021
• Publicly Available Date: Mar 3, 2021
• Journal: Symmetry
• Electronic ISSN: 2073-8994
• Publisher: MDPI
• Peer Reviewed: Peer Reviewed
• Volume: 12
• Issue: 1
• Pages: 118
• DOI: https://doi.org/10.3390/sym12010118
• Keywords: probability distributions, elliptical distributions, skew-elliptical distributions, flexible parametric distributions