A Characterization of a Matric‐Variate Exponential Distribution

Donald St P. Richards

doi:10.1111/j.1467-842X.1981.tb00782.x

A Characterization of a Matric‐Variate Exponential Distribution

Donald St P. Richards

Statistics

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Abstract

Suppose S is a positive definite m x m random matrix and S> Ω denotes the event that S—Ω is positive definite, Ω being a constant positive definite matrix. Under very mild regularity conditions, we show that the constraint Pr(S>Ω₁+Ω₂ | S>Ω₂) = Pr(S>Ω₁) implies that S has a Wishart distribution on m+ 1 degrees of freedom.

Original language	English (US)
Pages (from-to)	238-239
Number of pages	2
Journal	Australian Journal of Statistics
Volume	23
Issue number	2
DOIs	https://doi.org/10.1111/j.1467-842X.1981.tb00782.x
State	Published - Jun 1981

All Science Journal Classification (ASJC) codes

Statistics and Probability

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10.1111/j.1467-842X.1981.tb00782.x

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abstract = "Suppose S is a positive definite m x m random matrix and S> Ω denotes the event that S—Ω is positive definite, Ω being a constant positive definite matrix. Under very mild regularity conditions, we show that the constraint Pr(S>Ω1+Ω2 | S>Ω2) = Pr(S>Ω1) implies that S has a Wishart distribution on m+ 1 degrees of freedom.",

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N2 - Suppose S is a positive definite m x m random matrix and S> Ω denotes the event that S—Ω is positive definite, Ω being a constant positive definite matrix. Under very mild regularity conditions, we show that the constraint Pr(S>Ω1+Ω2 | S>Ω2) = Pr(S>Ω1) implies that S has a Wishart distribution on m+ 1 degrees of freedom.

AB - Suppose S is a positive definite m x m random matrix and S> Ω denotes the event that S—Ω is positive definite, Ω being a constant positive definite matrix. Under very mild regularity conditions, we show that the constraint Pr(S>Ω1+Ω2 | S>Ω2) = Pr(S>Ω1) implies that S has a Wishart distribution on m+ 1 degrees of freedom.

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ER -

A Characterization of a Matric‐Variate Exponential Distribution

Abstract

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