## Abstract

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.

Original language | English |
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Pages (from-to) | 370-399 |

Number of pages | 30 |

Journal | Advances in Applied Probability |

Volume | 53 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 2021 |