On fundamental skew distributions

Authors:
Reinaldo B. Arellano-Valle;Marc G. Genton
Affiliations:
Departamento de Estadística, Pontificia Universidad Católica de Chile Casilla 306, Santiago 22, Chile;Department of Statistics, Texas A&M University, College station, TX 77843-3143, USA
Venue:
Journal of Multivariate Analysis
Year:
2005

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Abstract

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.