Estimation of the confidence interval for binomial proportion

Abstract

The problematic behavior of the coverage probability of standard interval for binomial proportion (p) has been pointed out in several research articles such as in Brown et al. [1, 2] and Agresti & Coull [3]. A number of researchers have invented alternative confidence intervals for p. Each interval is investigated its coverage probability and expected length. The aims of this paper are to: 1) introduce the new confidence interval for p without the chaotic coverage properties, and 2) study the characteristics of the existing confidence intervals for p. Simulations are used to generate random samples in comparison to coverage probability and expected length for each confidence interval. Based on this study, the recommendations are given on which confidence interval should be used in what circumstances.