Article ID Journal Published Year Pages File Type
1154153 Statistics & Probability Letters 2007 8 Pages PDF
Abstract

A remarkable characterization result concerning the real-Dirichlet distribution says that if X1,…,XqX1,…,Xq are real random variables, then (X1,…,Xq)(X1,…,Xq) has a Dirichlet joint distribution with parameters (p1,…,pq)(p1,…,pq) if and only if, for all positive real numbers f1,…,fqf1,…,fq,equation(0.1)E∑i=1qfiXi-(p1+⋯+pq)=∏i=1qfi-pi.The aim of the present paper is to extend this characterization to the Dirichlet distributions on positive definite symmetric matrices defined in Letac et al. [2001. An expectation formula for the multivariate Dirichlet distribution. J. Multivariate Anal. 77, 117–137].

Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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