We construct exact and optimal one-sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well-established optimality theory of Buehler. Starting with five different approximate lower and upper limits, we adjust them to have coverage probability exactly equal to the desired nominal level and then compare the resulting exact limit...

Correspondence K. Krishnamoorthy, Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, U.S.A. Email: [email protected] The problems of finding confidence limits for the mean and an upper percentile, and upper prediction limits for the mean of a future sample from a gamma distribution are considered. Simple methods based on cube root transformation and fiduci...