Contributions to Interval Estimation for Parameters of Discrete Distributions
- Author(s): Holladay, Bret Andrew
- Advisor(s): Jammalamadaka, Sreenivasa R
- et al.
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.