Generalized skew-elliptical distributions and their quadratic forms

Marc G. Genton*, Nicola M.R. Loperfido

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

133 Scopus citations


This paper introduces generalized skew-elliptical distributions (GSE), which include the multivariate skew-normal, skew-t, skew-Cauchy, and skew-elliptical distributions as special cases. GSE are weighted elliptical distributions but the distribution of any even function in GSE random vectors does not depend on the weight function. In particular, this holds for quadratic forms in GSE random vectors. This property is beneficial for inference from non-random samples. We illustrate the latter point on a data set of Australian athletes.

Original languageEnglish (US)
Pages (from-to)389-401
Number of pages13
JournalAnnals of the Institute of Statistical Mathematics
Issue number2
StatePublished - Jun 2005
Externally publishedYes


  • Elliptical distribution
  • Invariance
  • Kurtosis
  • Selection model
  • Skewness
  • Weighted distribution

ASJC Scopus subject areas

  • Statistics and Probability


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