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Short confidence intervals for the count parameters of the binomial, negative binomial, and hypergeometric distributions

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  • Bret A. Holladay
  • Mark F. Schilling

Abstract

We study interval estimation of the sample size parameter of the binomial and hypergeometric distributions and of the count parameter of the negative binomial distribution. We compare the performance of the analogs of some of the most notable confidence procedures in the literature, adapting these procedures to our setting. We consider only methods that maintain a coverage probability at or above the nominal confidence level, and in all cases analyzed we identify the procedure(s) attaining the shortest confidence interval length, as judged by cumulative average length and expected length. A link to a Shiny web app is provided for computing the recommended confidence intervals in practice.

Suggested Citation

  • Bret A. Holladay & Mark F. Schilling, 2025. "Short confidence intervals for the count parameters of the binomial, negative binomial, and hypergeometric distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 54(17), pages 5428-5442, September.
    • Handle: RePEc:taf:lstaxx:v:54:y:2025:i:17:p:5428-5442
    DOI: 10.1080/03610926.2024.2437503
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