Keywords

Bayesian statistical decision theory, Binomial distribution, Confidence intervals, hypergeometric distribution

Abstract

The objective of this thesis is to examine one of the most fundamental and yet important methodologies used in statistical practice, interval estimation of the probability of success in a binomial distribution. The textbook confidence interval for this problem is known as the Wald interval as it comes from the Wald large sample test for the binomial case. It is generally acknowledged that the actual coverage probability of the standard interval is poor for values of p near 0 or 1. Moreover, recently it has been documented that the coverage properties of the standard interval can be inconsistent even if p is not near the boundaries. For this reason, one would like to study the variety of methods for construction of confidence intervals for unknown probability p in the binomial case. The present thesis accomplishes the task by presenting several methods for constructing confidence intervals for unknown binomial probability p. It is well known that the hypergeometric distribution is related to the binomial distribution. In particular, if the size of the population, N, is large and the number of items of interest k is such that k/N tends to p as N grows, then the hypergeometric distribution can be approximated by the binomial distribution. Therefore, in this case, one can use the confidence intervals constructed for p in the case of the binomial distribution as a basis for construction of the confidence intervals for the unknown value k = pN. The goal of this thesis is to study this approximation and to point out several confidence intervals which are designed specifically for the hypergeometric distribution. In particular, this thesis considers several confidence intervals which are based on estimation of a binomial proportion as well as Bayesian credible sets based on various priors.

Notes

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Graduation Date

2011

Semester

Summer

Advisor

Pensky, Marianna

Degree

Master of Science (M.S.)

College

College of Sciences

Department

Mathematics

Format

application/pdf

Identifier

CFE0003919

URL

http://purl.fcla.edu/fcla/etd/CFE0003919

Language

English

Release Date

August 2011

Length of Campus-only Access

None

Access Status

Masters Thesis (Open Access)

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Included in

Mathematics Commons

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