Open Access
September, 1975 A Note on Substitution in Conditional Distribution
Michael D. Perlman, Michael J. Wichura
Ann. Statist. 3(5): 1175-1179 (September, 1975). DOI: 10.1214/aos/1176343248


The following proposition is sometimes used in distribution theory: for each fixed $z$ suppose that $T(X, z)$ has the distribution $Q$ and is independent of $Y$; then $T(X, Z(Y))$ has the distribution $Q$ and is independent of $Y$. An example is presented to show this result is false in general. Additional conditions under which the proposition becomes valid are presented.


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Michael D. Perlman. Michael J. Wichura. "A Note on Substitution in Conditional Distribution." Ann. Statist. 3 (5) 1175 - 1179, September, 1975.


Published: September, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0323.62009
MathSciNet: MR408077
Digital Object Identifier: 10.1214/aos/1176343248

Primary: 62E15
Secondary: 62H10

Keywords: conditional distribution , independence , matrix-variate beta , regular conditional probability , substitution , Wishart

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 5 • September, 1975
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