On fundamental skew distributions

Reinaldo B. Arellano-Valle; Marc G. Genton

doi:10.1016/j.jmva.2004.10.002

On fundamental skew distributions

Reinaldo B. Arellano-Valle, Marc G. Genton^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

263 Scopus citations

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.

Original language	English (US)
Pages (from-to)	93-116
Number of pages	24
Journal	JOURNAL OF MULTIVARIATE ANALYSIS
Volume	96
Issue number	1
DOIs	https://doi.org/10.1016/j.jmva.2004.10.002
State	Published - Sep 2005
Externally published	Yes

Keywords

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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10.1016/j.jmva.2004.10.002

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year = "2005",

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AU - Arellano-Valle, Reinaldo B.

AU - Genton, Marc G.

PY - 2005/9

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AB - 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.

KW - Marginal and conditional distributions

KW - Moment generating function

KW - Normal, spherical and elliptical distributions

KW - Quadratic forms

KW - Stochastic representation

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M3 - Article

AN - SCOPUS:19744374218

SN - 0047-259X

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EP - 116

JO - JOURNAL OF MULTIVARIATE ANALYSIS

JF - JOURNAL OF MULTIVARIATE ANALYSIS

IS - 1

ER -

On fundamental skew distributions

Abstract

Keywords

ASJC Scopus subject areas

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