COMPARISON OF 3 ESTIMATORS OF THE NUMBER OF SPECIES

We consider estimation of the number of cells in a multinomial distribution. This is one version of the species problem: there are many applications, such as the estimation of the number of unobserved species of animals; estimation of vocabulary size, etc. We describe the results of a simulation comparison of three principal 'frequentist' procedures for estimating the number of cells (or species). The first procedure postulates a functional form for the cell probabilities; the second procedure approximates the distribution of the probabilities by a parametric probability density function; and the third procedure is based on an estimate of the sample coverage, i.e. the sum of the probabilities of the observed cells. Among the procedures studied we find that the third (non-parametric) method is globally preferable; the second (functional parametric) method cannot be recommended; and that, when based on the inverse Gaussian density, the first method is competitive in some cases with the third method. We also discuss Sichel's recent generalized inverse Gaussian-based procedure which, with some refinement, promises to perform at least as well as the non-parametric method in all cases.