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Abstract:
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This paper introduces mean-minimum (MM) exact confidence intervals for a binomial probability. These intervals, which can be classified as exact or approximate, guarantee that the mean and minimum frequentist coverage never drop below specified values. For example, an MM exact 95[93]% interval has mean coverage at least 95% and minimum coverage at least 93%. In the conventional sense, such an interval can be viewed as both an exact 93% and an approximate 95% interval. Graphical and numerical summaries of coverage and expected length suggest that the Blaker-based MM exact interval is an attractive alternative to, even an improvement over, commonly recommended approximate and exact intervals, including the Agresti-Coull approximate interval, the Clopper-Pearson (CP) exact interval, and the more recently recommended CP-, Blaker-, and Sterne-based mean-coverage-adjusted approximate intervals.
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