Dirichlet distribution through neutralities with respect to two partitions

Different concepts of neutrality have been studied in the literature in context of independence properties of vectors of random probabilities, in particular, for Dirichlet random vectors. Some neutrality conditions led to characterizations of the Dirichlet distribution. In this paper we provide a new characterization in terms of neutrality with respect to two partitions, which generalizes previous results. In particular, no restrictions on the size of the vector of random probabilities are imposed. In the proof we enhance the moments method approach proposed in Bobecka and Wesołowski (2009) [2] by combining it with some graph theoretic techniques.