Closed Form Prediction Intervals for a Binomial Random Variable

A prediction interval for a binomial random variable is an important tool in many industry applications. The performance of the existing prediction intervals, however, are unsatisfactory when the true binomial proportion is near a boundary. Since the true proportion can be very small in real applications, in this study, we propose improved prediction intervals with better coverage probability than the existing methods. Their predictive distributions are compared in terms of Kullback-Leibler distance criterion and the proposed intervals are illustrated by a real data example.