This leads us to consideration of alternative intervals. A number of natural alternatives are presented, each with its motivation and context. Each interval is examined as regards its coverage probability and its length. Based on this analysis, we recommend the Wilson interval (Wilson (1927)) or the equal tailed Jeffreys prior interval for small n, and the interval suggested in Agresti and Coull (1998) for larger n. We also provide an additional frequentist justification for use of the Jeffreys interval.
Brown, L.D., Cai, T. & DasGupta, A. (2002).
Confidence intervals for a binomial proportion and asymptotic expansions.
The Annals of Statistics 30, 160-201.
Brown, L.D., Cai, T. & DasGupta, A. (2003).
Interval estimation in exponential families.
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Cai, T. (2005).
One-sided confidence intervals in discrete distributions.
J. Statistical Planning and Inference 131, 63-88.