Confidence Intervals for the Product of Two Binomial Parameters

Abstract Many more-or-less reasonable solutions to the problem of statistical estimation of the product P 1 P 2 of two binomial parameters by confidence intervals can be given. After specializing to the case where P 1 and P 2 are much less than 1 and to estimation by "one-sided" intervals it is shown that a unique solution is obtained when one assumes a certain set of inequalities and then requires the intervals to be as short as possible. Tables of intervals for 90 and 95 per cent confidence levels are presented based on reasonable sets of inequalities and on a Poisson approximation to the binomial.