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Exact Optimal Confidence Intervals for Hypergeometric Parameters

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  • Weizhen Wang

Abstract

For a hypergeometric distribution, denoted by , where N is the population size, M is the number of population units with some attribute, and n is the given sample size, there are two parametric cases: (i) N is unknown and M is given; (ii) M is unknown and N is given. For each case, we first show that the minimum coverage probability of commonly used approximate intervals is much smaller than the nominal level for any n , then we provide exact smallest lower and upper one-sided confidence intervals and an exact admissible two-sided confidence interval, a complete set of solutions, for each parameter. Supplementary materials for this article are available online.

Suggested Citation

  • Weizhen Wang, 2015. "Exact Optimal Confidence Intervals for Hypergeometric Parameters," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1491-1499, December.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:512:p:1491-1499
    DOI: 10.1080/01621459.2014.966191
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    1. Huwang, Longcheen, 1995. "A note on the accuracy of an approximate interval for the binomial parameter," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 177-180, August.
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