Skew-symmetric and generalized skew-elliptical distributions

Marc G. Genton*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

14 Scopus citations


A popular approach to model departures from normality consists of modifying a symmetric probability density function (pdf) of a random variable, or of a random vector in the multivariate setting, in a multiplicative fashion, thereby introducing skewness. This idea has been in the literature for a long time, but it has been thoroughly implemented for the univariate normal distribution by Azzalini (1985, 1986), yielding the so-called skew-normal distribution. An extension to the multivariate case was then introduced by Azzalini and Dalla Valle (1996). Statistical applications of the multivariate skew-normal distribution were presented by Azzalini and Capitanio (1999), who also briefly discussed an extension to elliptical densities. Since then, several authors have tried to generalize these results to skewing arbitrary symmetric pdf’s with very general forms of multiplicative functions.

Original languageEnglish (US)
Title of host publicationSkew-Elliptical Distributions and Their Applications
Subtitle of host publicationA Journey Beyond Normality
PublisherCRC Press
Number of pages20
ISBN (Electronic)9780203492000
ISBN (Print)9781584884316
StatePublished - Jan 1 2004

Bibliographical note

Publisher Copyright:
© 2004 by Taylor & Francis Group, LLC.

ASJC Scopus subject areas

  • General Mathematics


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