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Generalized Poisson–Dirichlet distributions based on the Dickman subordinator
R. Mallera, S. Shemehsavarbcd a Research School of Finance, Actuarial Studies and Statistics, Australian
National University, Acton, Australia
b Australian National University, Australia
c University of Tehran, Iran
d Murdoch University, Australia
Abstract:
We study exchangeable random partitions based on an underlying Dickman
subordinator and the corresponding family of Poisson–Dirichlet distributions.
The large sample distribution of the vector representing the block sizes and the
number of blocks in a partition of $\{1,2,\dots,n\}$ is shown to be, after
norming and centering, a product of independent Poissons and a normal
distribution. In a species or gene sampling situation, these quantities
represent the abundances and the numbers of species or genes observed in
a sample of size $n$ from the corresponding Poisson–Dirichlet distribution. We
include a summary of known convergence results concerning the Dickman
subordinator in this context.
Keywords:
exchangeable random partitions, generalized Poisson–Dirichlet laws, negative binomial point process, Dickman subordinator and distribution, species sampling models, Ewens sampling formula.
Received: 25.11.2020 Revised: 12.03.2021 Accepted: 15.03.2021
Citation:
R. Maller, S. Shemehsavar, “Generalized Poisson–Dirichlet distributions based on the Dickman subordinator”, Teor. Veroyatnost. i Primenen., 67:4 (2022), 745–767; Theory Probab. Appl., 67:4 (2022), 593–612
Linking options:
https://www.mathnet.ru/eng/tvp5460https://doi.org/10.4213/tvp5460 https://www.mathnet.ru/eng/tvp/v67/i4/p745
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Abstract page: | 154 | Full-text PDF : | 20 | References: | 58 | First page: | 6 |
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