Exact confidence coefficients of confidence intervals for a binomial proportion

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 <= p <= 1) P-p (p is an element of (L(X), U(X))). Usually, the exact confidence coefficient is unknown since the infimum of the coverage probabilities may occur at any point p E (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.