Explicit Formula for Constructing Binomial Confidence Interval with Guaranteed Coverage Probability

TL;DR

This paper presents an explicit formula for binomial confidence intervals that guarantees coverage probability and is tighter than traditional methods, improving accuracy over normal approximation.

Contribution

It introduces a novel explicit formula for binomial confidence intervals with guaranteed coverage, surpassing normal approximation and classic methods like Clopper-Pearson.

Findings

The formula guarantees coverage probability.

It produces narrower intervals than Clopper-Pearson.

Approximate formulas perform well in coverage accuracy.

Abstract

In this paper, we derive an explicit formula for constructing the confidence interval of binomial parameter with guaranteed coverage probability. The formula overcomes the limitation of normal approximation which is asymptotic in nature and thus inevitably introduce unknown errors in applications. Moreover, the formula is very tight in comparison with classic Clopper-Pearson's approach from the perspective of interval width. Based on the rigorous formula, we also obtain approximate formulas with excellent performance of coverage probability.