An integral characterization of the Dirichlet process

TL;DR

This paper introduces a novel integral characterization of the Dirichlet process on general phase spaces, utilizing size-biased sampling to connect with Beta and Poisson-Dirichlet distributions, advancing understanding of these stochastic processes.

Contribution

It provides a new integral characterization of the Dirichlet process and links it with size-biased sampling, Beta distribution, and Poisson-Dirichlet distribution.

Findings

Characterization of the nonsymmetric Beta distribution via size-biased sampling

New integral characterization of the Dirichlet distribution

Marked version of classical Poisson-Dirichlet characterization

Abstract

We give a new integral characterization of the Dirichlet process on a general phase space. To do so we first prove a characterization of the nonsymmetric Beta distribution via size-biased sampling. Two applications are a new characterization of the Dirichlet distribution and a marked version of a classical characterization of the Poisson-Dirichlet distribution via invariance under size-biased sampling.