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Teoriya Veroyatnostei i ee Primeneniya, 2022, Volume 67, Issue 4, Pages 745–767
DOI: https://doi.org/10.4213/tvp5460
(Mi tvp5460)
 

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
References:
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
English version:
Theory of Probability and its Applications, 2022, Volume 67, Issue 4, Pages 593–612
DOI: https://doi.org/10.1137/S0040585X97T991167
Bibliographic databases:
Document Type: Article
Language: Russian
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
Citation in format AMSBIB
\Bibitem{MalShe22}
\by R.~Maller, S.~Shemehsavar
\paper Generalized Poisson--Dirichlet distributions based on the Dickman subordinator
\jour Teor. Veroyatnost. i Primenen.
\yr 2022
\vol 67
\issue 4
\pages 745--767
\mathnet{http://mi.mathnet.ru/tvp5460}
\crossref{https://doi.org/10.4213/tvp5460}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4548665}
\transl
\jour Theory Probab. Appl.
\yr 2022
\vol 67
\issue 4
\pages 593--612
\crossref{https://doi.org/10.1137/S0040585X97T991167}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85153254735}
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  • https://doi.org/10.4213/tvp5460
  • https://www.mathnet.ru/eng/tvp/v67/i4/p745
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    Теория вероятностей и ее применения Theory of Probability and its Applications
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