Generalized skew-elliptical distributions and their quadratic forms

Marc G. Genton; Nicola M.R. Loperfido

doi:10.1007/BF02507031

Generalized skew-elliptical distributions and their quadratic forms

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

^*Corresponding author for this work

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

134 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	389-401
Number of pages	13
Journal	Annals of the Institute of Statistical Mathematics
Volume	57
Issue number	2
DOIs	https://doi.org/10.1007/BF02507031
State	Published - Jun 2005
Externally published	Yes

Keywords

Elliptical distribution
Invariance
Kurtosis
Selection model
Skewness
Weighted distribution

ASJC Scopus subject areas

Statistics and Probability

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10.1007/BF02507031

Cite this

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abstract = "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.",

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AU - Genton, Marc G.

AU - Loperfido, Nicola M.R.

PY - 2005/6

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N2 - 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.

AB - 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.

KW - Elliptical distribution

KW - Invariance

KW - Kurtosis

KW - Selection model

KW - Skewness

KW - Weighted distribution

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JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

IS - 2

ER -

Generalized skew-elliptical distributions and their quadratic forms

Abstract

Keywords

ASJC Scopus subject areas

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