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Sampling from Dirichlet partitions: estimating the number of species
Author(s) -
Huillet Thierry,
Paroissin Christian
Publication year - 2009
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.977
Subject(s) - dirichlet distribution , mathematics , estimator , poisson distribution , statistics , sampling (signal processing) , stratified sampling , poisson sampling , generalized dirichlet distribution , sampling distribution , concentration parameter , importance sampling , slice sampling , dirichlet series , computer science , mathematical analysis , monte carlo method , filter (signal processing) , computer vision , boundary value problem
The Dirichlet partition of an interval can be viewed as the generalization of several classical models in ecological statistics. We recall the unordered Ewens sampling formulae ‐ESF) 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 ‐PD) distribution. To conclude with, we apply the different estimators suggested to two different sets of real data. Copyright © 2009 John Wiley & Sons, Ltd.