Confidence intervals for a bounded mean in exponential families

Setting confidence bounds or intervals for a parameter in a restricted parameter space is an important issue in applications and is widely discussed in the recent literature. In this article, we focus on the distributions in the exponential families, and propose general forms of the truncated Pratt interval and rp interval for the means. We take the Poisson distribution as an example to illustrate the method and compare it with the other existing intervals. Besides possessing the merits from the theoretical inferences, the proposed intervals are also shown to be competitive approaches from simulation and real-data application studies.