Contributions to Interval Estimation for Parameters of Discrete Distributions
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.