A new parametrization of the Gnedin-Fisher species sampling model

TL;DR

This paper introduces a new parametrization for a species sampling model that allows for finite but random numbers of species, providing a new representation and structural distribution analysis.

Contribution

It presents a novel parametrization of the Gnedin-Fisher species sampling model, linking it to generalized Waring mixtures and deriving its structural distribution.

Findings

Reparametrization yields a generalized Waring mixture representation.

Derived the structural distribution of the new model.

Provides insights into finite but random species diversity.

Abstract

We introduce a new parametrization for the two-parameter species sampling model with {\it finite} but {\it random} number of different species recently introduced in Gnedin (2010a). We show the reparametrization yields a representation in terms of generalized Waring mixture of Fisher species sampling models and derive the structural distribution of the model.