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 λ of a Poisson distribution. In thi...

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Veröffentlicht in:Journal of applied statistics Jg. 52; H. 3; S. 687 - 701
Hauptverfasser: Wang, Weizhen, Yu, Chongxiu, Zhang, Zhongzhan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: England Taylor & Francis 2025
Taylor & Francis Ltd
Schlagworte:
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
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Zusammenfassung: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.
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ISSN:0266-4763
1360-0532
DOI:10.1080/02664763.2024.2392105