Confidence Intervals for the Scale Parameter of Exponential Family of Distributions

This article presents a unified approach for computing nonequal tail optimal confidence intervals (CIs) for the scale parameter of the exponential family of distributions. We prove that there exists a pivotal quantity, as a function of a complete sufficient statistic, with a chi-square distribution. Using the similarity between equations of shortest, unbiased, and highest density CIs, all equations are reduced into a system of two equations that can be solved via a straightforward algorithm.