Nonparametric Estimations about Species Not Observed in a Random Sample

A brief survey of work done on two long-standing and important problems in statistics is given. In a simple random sample (with replacement) of size n from a population divided into species, if N distinct species are observed, what is the probability that, on the next trial, a species not observed before is discovered? And what is the total number of species not observed? Interesting in many applied areas, these problems have been discussed in a great number of papers. We survey some of the related publications as well as a Bayes-like estimator recently devised by the authors, together with results on the estimation of the distribution of the probability of discovering a new species.