#### 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)

#### STARS Citation

Mojica, Irene, "Exploring Confidence Intervals in the Case of Binomial and Hypergeometric Distributions" (2011). *Electronic Theses and Dissertations, 2004-2019*. 6644.

https://stars.library.ucf.edu/etd/6644