A sample of N units is taken from a population consisting of an unknown number of species. We are interested in estimating the number of species and the prediction function for future sampling. The prediction function is defined as the expected number of new species that will be found if an additional sample of size t N is taken for any positive real number t. In this paper we point out that an estimator suggested by Efron and Thisted lacks some essential properties of the true prediction function, for example, the property of alternating copositivity. As a result it cannot be used for large values of t. We propose an alternative estimator that possesses the essential properties and is easily obtained. We illustrate our estimator with two numerical examples and a simulation study.
A set of items is called group‐testable if for any subset of these items it is possible to carry out a simultaneous test with two possible outcomes: “success,” indicating that all items in the subset are good, and “failure,” indicating a contaminated subset. In this article we compare two alternatives of purchasing group‐testable items in order to meet a demand of d good items. These two alternatives are (i) purchasing d good items from a 100% quality population with a relatively high cost per item, and (ii) purchasing N items, N>d, from a 100q% (0
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