Abstract
Abstract A random sample is taken from a population consisting of an unknown number of distinct species. A quantity of interest is the probability of discovering a new species when an additional draw from the population is made. An estimator of this quantity was introduced by Starr (1979). We prove a conjecture of Starr's that the estimator is uniformly minimum variance unbiased and give various asymptotic properties of the estimator. A nonparametric maximum likelihood estimator that has similar asymptotic properties is introduced. A Monte Carlo study that suggests guidelines for choosing an estimator under various circumstances is given. To amplify, suppose that if we take a sample of size 1 from a population then the probability of drawing a representative of the ith species is p 1. If n draws are made with replacement, the (unconditional) probability that species i will be observed for the first time on the n + 1st draw is given simply as the term p i q n i (q i = 1 − p i ) from a geometric distributio...
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