UC Santa Barbara

We study interval estimation for parameters of discrete distributions, focusing on the

binomial, Poisson, negative binomial, and hypergeometric distributions explicitly. We

provide a broad treatment of the problem, covering both conventional and randomized

confidence 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 probability

functions and determine the optimal procedure under each of a wide variety of criteria,

including multiple notions of length. Several new methods are proposed, including a

method that produces length optimal fuzzy confidence intervals. Credible intervals and

multi-parameter discrete distributions are also considered.