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Contributions to Interval Estimation for Parameters of Discrete Distributions

  • Author(s): Holladay, Bret Andrew
  • Advisor(s): Jammalamadaka, Sreenivasa R
  • et al.
Abstract

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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