Sampling from Dirichlet populations: estimating the number of species

Thierry Huillet (1) , Christian Paroissin (2)

1 LPTM - UMR 8089 - Laboratoire de Physique Théorique et Modélisation
2 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

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.

Mots clés: estimated number of species from sampling; random discrete distribution; Dirichlet partition; GEM; Ewens sampling formulae

Domaines: Méthodologie [stat.ME]; Ecosystèmes; Théorie [stat.TH]; Statistiques [math.ST]

Thierry Huillet, Christian Paroissin. Sampling from Dirichlet populations: estimating the number of species. 2007. ⟨hal-00320181⟩