A generalised Dickman distribution and the number of species in a negative binomial process model

We derive the large-sample distribution of the number of species in a version of Kingman's Poisson-Dirichlet model constructed from an -stable subordinator but with an underlying negative binomial process instead of a Poisson process. Thus it depends on parameters from the subordinator and 0$ ]]> from the negative binomial process. The large-sample distribution of the number of species is derived as sample size. 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.