A Generalized Dickman Distribution and the Number of Species in a Negative Binomial Process Model

Abstract: In Ipsen, Maller, Shemehsavar (J. Theoret. Prob., 2019) we defined a new class of distributions related to Kingman’s PD$_\alpha $ distribution, which we called PD$_\alpha ^{(r)}$. It has two parameters, $\alpha\in (0,1)$ and $r > 0.$

A version of Ewens’ sampling formula was derived for it, and we obtained a formula for the probability mass function of Kn, the number of allele types/species observed in a sample of size n from PD$_\alpha ^{(r)}$.

The aim of this seminar is to sketch a derivation of the large-sample distribution of $K_n$ as $n \to\infty$.

We cite a set of genetics data on the near-threatened marsupial quoll as a nice motivation. [Joint work with Yuguang Ipsen and Soudabeh Shemehsavar.]

probability

Audience: researchers in the topic

Probability Victoria Seminar (PVSeminar)

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