Exact Optimal Confidence Intervals for Hypergeometric Parameters

Weizhen Wang

Journal of the American Statistical Association, 2015, vol. 110, issue 512, 1491-1499

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.

Date: 2015
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DOI: 10.1080/01621459.2014.966191

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