Closure of beta and Dirichlet distributions under discrete mixing

N. Balakrishnan and M.C. Jones

Statistics & Probability Letters, 2022, vol. 188, issue C

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.

Keywords: Beta binomial mixture; Beta negative binomial mixture; Dirichlet multinomial mixture; Libby–Novick distribution; Sibuya distribution; Winsorized distributions (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2022.109526

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