Award Date

5-2011

Degree Type

Thesis

Degree Name

Master of Science in Mathematical Science

Department

Mathematical Sciences

First Committee Member

Hokwon Cho, Chair

Second Committee Member

Malwane Ananda

Third Committee Member

Sandra Catlin

Graduate Faculty Representative

Chad Cross

Number of Pages

44

Abstract

We study measures of a comparison for two independent binomial variates which frequently occur in real situations. An estimator for measure of reduction (MOR) is considered for two sample proportions based on a modified maximum likelihood estimation. We study the desirable properties of the estimator: the asymptotic behavior of its unbiasedness and the variance of the estimator. Since the measure ρ is approximately normally distributed when sample sizes are sufficiently large, one may establish approximate confidence intervals for the true value of the estimators. For numerical study, the Monte Carlo experiment is carried out for the various scenarios of two sets of samples as well as to examine its finite sample behavior. Also, we investigate the behavior of the estimates when sample sizes get large. Two examples are provided to illustrate the use of this new measure, and extended to the hypothesis testing for further statistical inference.

Keywords

Binomial; Binomial distribution; Binomial theorem; Inference; Mathematical statistics; Measure; Probabilities; Random variables; Reduction; Statistical; Variates

Disciplines

Mathematics | Multivariate Analysis | Statistics and Probability

Language

English


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