A generalized score confidence interval for a binomial proportion

Constructing a confidence interval for a binomial proportion is one of the most basic problems in statistics. The score interval as well as the Wilson interval with some modified forms have been broadly investigated and suggested by many statisticians. In this paper, a generalized score interval CIG(a) is proposed by replacing the coefficient 1/4 in the score interval with parameter a. Based on analyzing and comparing various confidence intervals, we recommend the generalized score interval CIG(0.3) for the nominal confidence levels 0.90, 0.95 and 0.99, which improves the spike phenomenon of the score interval and behaves better and computes more easily than most of other approximate intervals such as the Agresti–Coull interval and the Jeffreys interval to estimate a binomial proportion.