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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.

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