Explicit Formula for Constructing Binomial Confidence Interval with Guaranteed Coverage Probability

Details Explicit Formula for Constructing Binomial Confidence Interval with Guaranteed Coverage Probability Explicit Formula for Constructing Binomial Confidence Interval with Guaranteed Coverage Probability

2007-07-05

arxiv.org/abs/0707.0837v1

Communications in Statistics -- Theory and Methods, vol. 37, pp. 1173--1180, 2008

Mathematics

Statistics Theory

20 pages, 27 figures

Scientific paper

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.

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