Closure of beta and Dirichlet distributions under discrete mixing

Balakrishnan, N. and Jones, M.C. (2022). Closure of beta and Dirichlet distributions under discrete mixing. Statistics & Probability Letters, 188, article no. 109526.

DOI: https://doi.org/10.1016/j.spl.2022.109526

Abstract

We identify a general approach to the construction of discrete mixtures of beta distributions that are themselves beta distributions, and explore a number of examples. The approach extends to discrete mixtures of transformed beta – so-called 'beta-G' – distributions that are themselves beta-G distributions, and to discrete mixtures of Dirichlet distributions that are Dirichlet distributions. Along the way, we make novel observations concerning the Sibuya distribution and introduce some new 'Winsorized' distributions.

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