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Closure of beta and Dirichlet distributions under discrete mixing

Author

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  • Balakrishnan, N.
  • Jones, M.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.

Suggested Citation

  • Balakrishnan, N. & Jones, M.C., 2022. "Closure of beta and Dirichlet distributions under discrete mixing," Statistics & Probability Letters, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:stapro:v:188:y:2022:i:c:s0167715222000980
    DOI: 10.1016/j.spl.2022.109526
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    References listed on IDEAS

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    1. Tomasz J. Kozubowski & Krzysztof Podgórski, 2018. "A generalized Sibuya distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 855-887, August.
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    5. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    6. A. Childs & B. Chandrasekar & N. Balakrishnan & D. Kundu, 2003. "Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 319-330, June.
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