Geodesic
Generalized Poisson–Dirichlet distributions based on the Dickman subordinator
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 4, pp. 745-767 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Mots-clés : exchangeable random partitions, negative binomial point process
Keywords: generalized Poisson–Dirichlet laws, Dickman subordinator and distribution, species sampling models, Ewens sampling formula. 
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R. Maller; S. Shemehsavar. Generalized Poisson–Dirichlet distributions based on the Dickman subordinator. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 4, pp. 745-767. http://geodesic.mathdoc.fr/item/TVP_2022_67_4_a5/

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