A new approach to precise interval estimation for the parameters of the hypergeometric distribution

Abstract

We study interval estimation for both parameters of the hypergeometric distribution: (i) the number of successes in a finite population and (ii) the size of the population. In contrast to traditional methods that specify intervals via a formula, our approach is to first establish the coverage probability function of an ideal procedure. This in turn determines the set of confidence intervals. In the case when the population size is known and we wish to estimate the number of successes, our approach is superior to existing methods in terms of average interval length and in fact achieves the minimum possible average length. In the case of estimating population size, our procedure also tends to produce shorter intervals than existing methods. Both procedures also possess an attractive coverage property.