The Shortest Clopper–Pearson Randomized Confidence Interval for Binomial Probability

Abstract

Zieli´nski (2010) showed the existence of the shortest Clopper–Pearson confidence interval for binomial probability. The method of obtaining such an interval was presented as well. Unfortunately, the confidence interval obtained has one disadvantage: it does not keep the prescribed confidence level. In this paper, a small modification is introduced, after which the resulting shortest confidence interval does not have the above mentioned disadvantage.

Keywords

• binomial proportion
• confidence interval
• shortest confidence intervals