A New Approach to Precise Interval Estimation for the Parameters of the Hypergeometric Distribution

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 confidence intervals. In the case when the population is known and we wish to estimate the number of successes, we find that our approach performs better than preexisting methods in terms of coverage and average length. The precise nature of our confidence procedure for the success parameter near small values of success (failure) indicates a particular usefulness, for example, in the field of medicine. In the case of estimating the population size, we also find that our procedure performs better in terms of coverage probability and length in comparison to a significant existing method. Applications are given to ecology and medicine.