Sampling from Dirichlet populations: estimating the number of species

TL;DR

This paper investigates estimating the number of species in Dirichlet populations by analyzing the distribution of distinct visited species, using statistical methods aligned with Poisson-Dirichlet sampling theory, and applies these estimators to real data.

Contribution

It introduces new estimators for the number of species in Dirichlet populations based on frequency distributions and validates them with real data applications.

Findings

Estimators align with Poisson-Dirichlet sampling theory.

Effective in real data applications.

Provides insights into species richness estimation.

Abstract

Consider the random Dirichlet partition of the interval into $n$ fragments with parameter $\theta >0$. We recall the unordered Ewens sampling formulae from finite Dirichlet partitions. As this is a key variable for estimation purposes, focus is on the number of distinct visited species in the sampling process. These are illustrated in specific cases. We use these preliminary statistical results on frequencies distribution to address the following sampling problem: what is the estimated number of species when sampling is from Dirichlet populations? The obtained results are in accordance with the ones found in sampling theory from random proportions with Poisson-Dirichlet distribution. To conclude with, we apply the different estimators suggested to two different sets of real data.