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

• Published in: Journal of applied statistics Vol. 52; no. 3; pp. 687 - 701
• Main Authors: Wang, Weizhen, Yu, Chongxiu, Zhang, Zhongzhan
• Format: Journal Article
• Language: English
• Published: England Taylor & Francis 2025; Taylor & Francis Ltd
• Subjects: 62-08; Algorithms; Bisection method; Clopper-Pearson-type interval; Confidence intervals; exact confidence interval; infimum coverage probability; monotonic confidence limits; Parameters; Poisson distribution; Statistical analysis; monotonic confidence limits; Clopper-Pearson-type interval; infimum coverage probability; 62-08; Bisection method; 62F99; exact confidence interval
• ISSN: 0266-4763; 1360-0532; 1360-0532
• DOI: 10.1080/02664763.2024.2392105

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 λ 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.