The Inverse Problem of Multivariate and Matrix-Variate Skew Normal Distributions

Shimin Zheng; J. M. Hardin; A. K. Gupta

doi:10.1080/02331888.2010.528895

The Inverse Problem of Multivariate and Matrix-Variate Skew Normal Distributions

Shimin Zheng
, J. M. Hardin
, A. K. Gupta

Department of Biostatistics and Epidemiology

University of Alabama
Bowling Green State University

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

Abstract

In this paper, we prove that the joint distribution of random vectors Z ₁ and Z ₂ and the distribution of Z ₂ are skew normal provided that Z ₁ is skew normally distributed and Z ₂ conditioning on Z ₁ is distributed as closed skew normal. Also, we extend the main results to the matrix variate case.

Original language	American English
Journal	Statistics
Volume	46
DOIs	https://doi.org/10.1080/02331888.2010.528895
State	Published - Jun 1 2012

Keywords

Primary: 62H10
Secondary: 62H05
closed skew normal distribution
conditional distribution
matrix variate skew normal distribution
matrix-variate closed skew normal distribution
multivariate distribution
normal distribution
skew normal distribution

Disciplines

Biostatistics
Mathematics

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10.1080/02331888.2010.528895License: Unspecified

https://doi.org/10.1080/02331888.2010.528895

Cite this

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title = "The Inverse Problem of Multivariate and Matrix-Variate Skew Normal Distributions",

abstract = " In this paper, we prove that the joint distribution of random vectors Z 1 and Z 2 and the distribution of Z 2 are skew normal provided that Z 1 is skew normally distributed and Z 2 conditioning on Z 1 is distributed as closed skew normal. Also, we extend the main results to the matrix variate case.",

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AU - Hardin, J. M.

AU - Gupta, A. K.

PY - 2012/6/1

Y1 - 2012/6/1

N2 - In this paper, we prove that the joint distribution of random vectors Z 1 and Z 2 and the distribution of Z 2 are skew normal provided that Z 1 is skew normally distributed and Z 2 conditioning on Z 1 is distributed as closed skew normal. Also, we extend the main results to the matrix variate case.

AB - In this paper, we prove that the joint distribution of random vectors Z 1 and Z 2 and the distribution of Z 2 are skew normal provided that Z 1 is skew normally distributed and Z 2 conditioning on Z 1 is distributed as closed skew normal. Also, we extend the main results to the matrix variate case.

KW - Primary: 62H10

KW - Secondary: 62H05

KW - closed skew normal distribution

KW - conditional distribution

KW - matrix variate skew normal distribution

KW - matrix-variate closed skew normal distribution

KW - multivariate distribution

KW - normal distribution

KW - skew normal distribution

UR - https://dc.etsu.edu/etsu-works/47

UR - https://doi.org/10.1080/02331888.2010.528895

U2 - 10.1080/02331888.2010.528895

DO - 10.1080/02331888.2010.528895

M3 - Article

VL - 46

JO - Statistics

JF - Statistics

ER -

The Inverse Problem of Multivariate and Matrix-Variate Skew Normal Distributions

Abstract

Keywords

Disciplines

Access to Document

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