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May, 1973 Two Characterizations of the Dirichlet Distribution
J. Fabius
Ann. Statist. 1(3): 583-587 (May, 1973). DOI: 10.1214/aos/1176342429

Abstract

Let $X = (X_1, \cdots, X_k)$ be a random vector with all $X_i \geqq 0$ and $\sum X_i \leqq 1$. Let $k \geqq 2$, and suppose that none of the $X_i$, nor $1 - \sum X_i$ vanishes almost surely. Without any further regularity assumptions, each of two conditions is shown to be necessary and sufficient for $X$ to be distributed according to a Dirichlet distribution or a limit of such distributions. Either condition requires that certain proportions between components of $X$ be independent of one or more other components of $X$.

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J. Fabius. "Two Characterizations of the Dirichlet Distribution." Ann. Statist. 1 (3) 583 - 587, May, 1973. https://doi.org/10.1214/aos/1176342429

Information

Published: May, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0257.62012
MathSciNet: MR353531
Digital Object Identifier: 10.1214/aos/1176342429

Subjects:
Primary: 62E10

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 3 • May, 1973
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