Published online by Cambridge University Press: 01 July 2021
We derive the large-sample distribution of the number of species in a version of Kingman’s Poisson–Dirichlet model constructed from an
$\alpha$
-stable subordinator but with an underlying negative binomial process instead of a Poisson process. Thus it depends on parameters
$\alpha\in (0,1)$
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
$n\to\infty$
. 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.