Investigation of a generalized multinomial model for species data

Abstract

The question of how to estimate the number of specie in a region given the species frequency distribution for a sample of animals from the region has been of interest for more than 60 years. Data analyses indicate that the inferential problem is a difficult one when there are many rare species and a few abundant ones. In this article simulation is used to study the properties of data sets generated by a generalized multinomial model proposed for this setting by Boender and Rinnooy Kan [Boender, C.G.E. and Rinnooy Kan, A.H.G., 1987, A multinomial Bayesian approach to the estimation of population and vocabulary size. Biometrika, 74, 849–856.]. In addition, the performance of Bayesian methods for drawing inferences about the parameters of the generalized multinomial model is evaluated by simulation.