Contributions to Interval Estimation for Parameters of Discrete Distributions

We study interval estimation for parameters of discrete distributions, focusing on thebinomial, Poisson, negative binomial, and hypergeometric distributions explicitly. Weprovide a broad treatment of the problem, covering both conventional and randomizedconfidence intervals, as well as Geyer and Meeden’s concept of fuzzy confidence intervals.We take a graphical approach to the problem through the use of coverage probabilityfunctions and determine the optimal procedure under each of a wide variety of criteria,including multiple notions of length. Several new methods are proposed, including amethod that produces length optimal fuzzy confidence intervals. Credible intervals andmulti-parameter discrete distributions are also considered