Correction to "Two Characterizations of the Dirichlet Distribution"

Abstract

Let X = (X1, ⋯, Xk) be a random vector with all Xi ≥ 0 and ∑ Xi ≤ 1. Let k ≥ 2, and suppose that none of the Xi, nor 1 - ∑ Xi 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.