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- W3208518480 abstract "The Ewens-Pitman sampling model (EP-SM) is a distribution for random partitions of the set ${1,ldots,n}$, with $ninmathbb{N}$, which is index by real parameters $alpha$ and $theta$ such that either $alphain[0,1)$ and $theta>-alpha$, or $alpha<0$ and $theta=-malpha$ for some $minmathbb{N}$. For $alpha=0$ the EP-SM reduces to the celebrated Ewens sampling model (E-SM), which admits a well-known compound Poisson perspective in terms of the log-series compound Poisson sampling model (LS-CPSM). In this paper, we consider a generalization of the LS-CPSM, which is referred to as the negative Binomial compound Poisson sampling model (NB-CPSM), and we show that it leads to extend the compound Poisson perspective of the E-SM to the more general EP-SM for either $alphain(0,1)$, or $alpha<0$. The interplay between the NB-CPSM and the EP-SM is then applied to the study of the large $n$ asymptotic behaviour of the number of blocks in the corresponding random partitions, leading to a new proof of Pitman's $alpha$ diversity. We discuss the proposed results, and conjecture that analogous compound Poisson representations may hold for the class of $alpha$-stable Poisson-Kingman sampling models, of which the EP-SM is a noteworthy special case." @default.
- W3208518480 created "2021-11-08" @default.
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- W3208518480 date "2021-11-04" @default.
- W3208518480 modified "2023-09-27" @default.
- W3208518480 title "A compound Poisson perspective of Ewens-Pitman sampling model." @default.
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