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Keywords:

  • binomial distribution;
  • confidence interval;
  • proportion

ABSTRACT

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 coverage adjustments of the Clopper–Pearson interval that incorporate prior or posterior beliefs into the interval. Using heatmap-type plots for comparing confidence intervals, we show that the coverage-adjusted intervals have satisfying coverage and shorter expected lengths than competing intervals found in the literature.