Fast algorithms of computing admissible intervals for discrete distributions with single parameter

It is of great interest to compute optimal exact confidence intervals for the success probability (p) in a binomial distribution, the number of subjects with a certain attribute (M) or the total number of subjects (N) in a hypergeometric distribution, and the mean lambda of a Poisson distribution. In this paper, efficient algorithms are proposed to compute an admissible exact interval for each of the four parameters when the sample size (n) or the random observation X is large. The algorithms are utilized in four practical examples: evaluating the relationship between two diseases, certifying companies, estimating the proportion of drug users, and analyzing earthquake frequency. The intervals computed by the algorithms are shorter, and the calculations are faster, demonstrating the accuracy of the results and the time efficiency of the proposed algorithms.