We search a population by selecting one member at a time with replacement and observing the species of each selected member. We are interested in predicting the conditional probability of discovering a new species in the next selection after $n$ observations. The existence and asymptotic behavior of the uniformly minimum variance unbiased estimator of the unconditional probability is investigated under the condition that the species are uniformly distributed. We also compare the performance of the estimator as a predictor of the conditional probability with that of a linear unbiased predictor.
"On Estimating the Probability of Discovering a New Species." Ann. Statist. 9 (6) 1339 - 1342, November, 1981. https://doi.org/10.1214/aos/1176345651