A Compound Poisson Perspective of Ewens–Pitman Sampling Model

The Ewens–Pitman sampling model (EP-SM) is a distribution for random partitions of the set {1,…,n}, with n∈N, which indexed by real parameters α and θ such that either α∈[0,1) θ>−α, or α<0 θ=−mα some m∈N. For α=0, EP-SM reduced to Ewens (E-SM), admits well-known compound Poisson perspective in terms log-series (LS-CPSM). In this paper, we consider generalisation LS-CPSM, referred as negative Binomial (NB-CPSM), show it leads an extension E-SM more general α∈(0,1), α<0. interplay between NB-CPSM then applied study large n asymptotic behaviour number blocks corresponding partitions—leading new proof Pitman’s diversity. We discuss proposed results conjecture analogous representations may hold class α-stable Poisson–Kingman models—of noteworthy special case.