A new estimator for the number of unobserved species in a random sample

We consider the classic problem of estimating T, the total number of species in a population, from repeated counts in a simple random sample. We first show that the frequently used Chao-Lee estimator can in fact be obtained by Bayesian methods with a Dirichlet prior, and then use such clarification to develop a new estimator which numerical tests and some real experiments show to be more flexibile than existing ones, in the sense that it is best at adapting to changes in the normalized interspecies variance 2. Our method involves simultaneous estimation of T, 2 and of the parameter in the Dirichlet prior, and the only limitation seems to come from the required convergence of the prior which imposes the restriction 2 1. The new estimator is easy to implement, the coverage frequency of confidence intervals based on resampling appears to be in good agreement with the desired confidence level, and we thus suggest that the present method could replace existing estimators in the absence of previous information on 2.