Limiting Distributions of Generalised Poisson–Dirichlet Distributions Based on Negative Binomial Processes

Yuguang Ipsen, Ross Maller, Soudabeh Shemehsavar*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    Abstract

    The PDα(r) distribution, a two-parameter distribution for random vectors on the infinite simplex, generalises the PD α distribution introduced by Kingman, to which it reduces when r= 0. The parameter α∈ (0 , 1) arises from its construction based on ratios of ordered jumps of an α-stable subordinator, and the parameter r> 0 signifies its connection with an underlying negative binomial process. Herein, it is shown that other distributions on the simplex, including the Poisson–Dirichlet distribution PD (θ) , occur as limiting cases of PDα(r), as r→ ∞. As a result, a variety of connections with species and gene sampling models, and many other areas of probability and statistics, are made.

    Original languageEnglish
    Pages (from-to)1974-2000
    Number of pages27
    JournalJournal of Theoretical Probability
    Volume33
    Issue number4
    DOIs
    Publication statusPublished - 1 Dec 2020

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