Tail-adjusted confidence intervals for a binomial proportion

Details Tail-adjusted confidence intervals for a binomial proportion Tail-adjusted confidence intervals for a binomial proportion

2012-04-26

arxiv.org/abs/1204.5894v1

Statistics

Methodology

25 pages, 14 figures, 1 table

Scientific paper

We consider the classic problem of interval estimation of a proportion $p$ based on binomial sampling. The "exact" Clopper-Pearson confidence interval for $p$ is known to be unnecessarily conservative. We propose tail-adjustments of the Clopper-Pearson interval using prior and posterior distributions of $p$. The adjusted intervals have improved coverage and are often shorter than competing intervals found in the literature. The tail-adjusted intervals are particularly suitable for $p$ close to 0 or 1. We study the asymptotic behaviour of the Clopper-Pearson interval and introduce new heatmap-type plots for comparing confidence intervals.

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