A proof for the existence of multivariate singular generalized skew-elliptical density functions

Tomer Shushi

doi:https://doi.org/10.1016/j.spl.2018.05.018

A proof for the existence of multivariate singular generalized skew-elliptical density functions

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Abstract

We derive the density functions of multivariate singular generalized skew-elliptical distributions, present their characteristic function, and derive explicit formulas for the expectation and the covariance matrix. This letter generalizes results given in Díaz-García et al. (2002) and Young et al. (2016) about the existence of multivariate singular elliptical and multivariate singular skew-normal density functions, respectively.

Original language	American English
Pages (from-to)	50-55
Number of pages	6
Journal	Statistics and Probability Letters
Volume	141
DOIs	https://doi.org/10.1016/j.spl.2018.05.018
State	Published - 1 Oct 2018
Externally published	Yes

Keywords

Affine subspace
Characteristic function
Generalized skew-elliptical distributions
High-dimensional data
Lebesgue measure
Pseudoinverse

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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Cite this

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keywords = "Affine subspace, Characteristic function, Generalized skew-elliptical distributions, High-dimensional data, Lebesgue measure, Pseudoinverse",

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AB - We derive the density functions of multivariate singular generalized skew-elliptical distributions, present their characteristic function, and derive explicit formulas for the expectation and the covariance matrix. This letter generalizes results given in Díaz-García et al. (2002) and Young et al. (2016) about the existence of multivariate singular elliptical and multivariate singular skew-normal density functions, respectively.

KW - Affine subspace

KW - Characteristic function

KW - Generalized skew-elliptical distributions

KW - High-dimensional data

KW - Lebesgue measure

KW - Pseudoinverse

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JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

A proof for the existence of multivariate singular generalized skew-elliptical density functions

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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