On fundamental skew distributions

Reinaldo B. Arellano-Valle, Marc Genton*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

252 Scopus citations


A new class of multivariate skew-normal distributions, fundamental skew-normal distributions and their canonical version, is developed. It contains the product of independent univariate skew-normal distributions as a special case. Stochastic representations and other main properties of the associated distribution theory of linear and quadratic forms are considered. A unified procedure for extending this class to other families of skew distributions such as the fundamental skew-symmetric, fundamental skew-elliptical, and fundamental skew-spherical class of distributions is also discussed.

Original languageEnglish (US)
Pages (from-to)93-116
Number of pages24
JournalJournal of Multivariate Analysis
Issue number1
StatePublished - Sep 1 2005


  • Marginal and conditional distributions
  • Moment generating function
  • Normal, spherical and elliptical distributions
  • Quadratic forms
  • Stochastic representation

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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