Statistica Sinica 17(2007), 361-368

EXACT CONFIDENCE COEFFICIENTS OF CONFIDENCE

INTERVALS FOR A BINOMIAL PROPORTION

Hsiuying Wang

Academia Sinica

Abstract: Let $X$ have a binomial distribution $B(n, p)$. For a confidence interval $(L(X), U(X))$ of a binomial proportion $p$, the coverage probability is a variable function of $p$. The confidence coefficient of the confidence interval is the infimum of the coverage probabilities, $\inf_{0 \leq p \leq 1}P_p (p \in (L(X), U(X)))$. Usually, the exact confidence coefficient is unknown since the infimum of the coverage probabilities may occur at any point $p\in (0, 1)$. In this paper, a methodology to compute the exact confidence coefficient is proposed. With this methodology, the point where the infimum of the coverage probabilities occurs, as well as the confidence coefficient, can be precisely derived.

Key words and phrases: Binomial distribution, confidence coefficient, confidence interval, coverage probability.