A generalized score confidence interval for a binomial proportion. (English) Zbl 1428.62122
Summary: 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 \(CI_{G(a)}\) 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 \(CI_{G(0.3)}\) 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.
MSC:
| 62F25 | Parametric tolerance and confidence regions |
Keywords:
binomial distribution; confidence interval; score interval; coverage probability; mean absolute error; average excepted length; standard deviationReferences:
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