A skew-symmetric representation of multivariate distributions

Jiuzhou Wang; Joseph Boyer; Marc G. Genton

A skew-symmetric representation of multivariate distributions

Jiuzhou Wang^*, Joseph Boyer, Marc G. Genton

^*Corresponding author for this work

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

105 Scopus citations

Abstract

This article studies a family of multivariate skew-symmetric distributions. We show that any multivariate probability density function admits a skew-symmetric representation. We derive several characteristics of this representation and establish an invariance property. We present a stochastic representation of skew-symmetric distributions which lends itself readily to simulations. The flexibility of skew-symmetric distributions is illustrated through several graphical examples.

Original language	English (US)
Pages (from-to)	1259-1270
Number of pages	12
Journal	STATISTICA SINICA
Volume	14
Issue number	4
State	Published - Oct 2004
Externally published	Yes

Keywords

Elliptical
Kurtosis
Multimodality
Quadratic form
Skewness
Stochastic representation

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

Cite this

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title = "A skew-symmetric representation of multivariate distributions",

abstract = "This article studies a family of multivariate skew-symmetric distributions. We show that any multivariate probability density function admits a skew-symmetric representation. We derive several characteristics of this representation and establish an invariance property. We present a stochastic representation of skew-symmetric distributions which lends itself readily to simulations. The flexibility of skew-symmetric distributions is illustrated through several graphical examples.",

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T1 - A skew-symmetric representation of multivariate distributions

AU - Wang, Jiuzhou

AU - Boyer, Joseph

AU - Genton, Marc G.

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N2 - This article studies a family of multivariate skew-symmetric distributions. We show that any multivariate probability density function admits a skew-symmetric representation. We derive several characteristics of this representation and establish an invariance property. We present a stochastic representation of skew-symmetric distributions which lends itself readily to simulations. The flexibility of skew-symmetric distributions is illustrated through several graphical examples.

AB - This article studies a family of multivariate skew-symmetric distributions. We show that any multivariate probability density function admits a skew-symmetric representation. We derive several characteristics of this representation and establish an invariance property. We present a stochastic representation of skew-symmetric distributions which lends itself readily to simulations. The flexibility of skew-symmetric distributions is illustrated through several graphical examples.

KW - Elliptical

KW - Kurtosis

KW - Multimodality

KW - Quadratic form

KW - Skewness

KW - Stochastic representation

UR - http://www.scopus.com/inward/record.url?scp=4043103972&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:4043103972

SN - 1017-0405

VL - 14

SP - 1259

EP - 1270

JO - STATISTICA SINICA

JF - STATISTICA SINICA

IS - 4

ER -

A skew-symmetric representation of multivariate distributions

Abstract

Keywords

ASJC Scopus subject areas

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