A generalised Dickman distribution and the number of species in a negative binomial process model. (June 2021) - Ipsen, Yuguang; Maller, Ross A.; Shemehsavar, Soudabeh
Abstract: We derive the large-sample distribution of the number of species in a version of Kingman's Poisson–Dirichlet model constructed from an $α$ -stable subordinator but with an underlying negative binomial process instead of a Poisson process. Thus it depends on parameters $α\in (0, 1)$ from the subordinator and $r>0$ from the negative binomial process. The large-sample distribution of the number of species is derived as sample size $n→∞$ . An important component in the derivation is the introduction of a two-parameter version of the Dickman distribution, generalising the existing one-parameter version. Our analysis adds to the range of Poisson–Dirichlet-related distributions available for modeling purposes.