#### Title

Exact Optimal Confidence Intervals for Hypergeometric Parameters

#### Document Type

Article

#### Publication Date

2015

#### Abstract

For a hypergeometric distribution, denoted by **Hyper*** (M,N,n), *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.

#### Repository Citation

Wang, W.
(2015). Exact Optimal Confidence Intervals for Hypergeometric Parameters. *Journal of the American Statistical Association, 110* (512), 1491-1499.

https://corescholar.libraries.wright.edu/math/299

#### DOI

10.1080/01621459.2014.966191