Improved closed-form prediction intervals for binomial and Poisson distributions

The problems of constructing prediction intervals for the binomial and Poisson distributions are considered. Available approximate, exact and conditional methods for both distributions are reviewed and compared. Simple approximate prediction intervals based on the joint distribution of the past samples and the future sample are proposed. Exact coverage studies and expected widths of prediction intervals show that the new prediction intervals are comparable to or better than the available ones in most cases. The methods are illustrated using two practical examples.