Date of Award

6-2009

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Dr. Magdalena Niewiadomska-Bugaj

Second Advisor

Dr. Joshua D. Naranjo

Third Advisor

Dr. Gerald L. Sievers

Fourth Advisor

Dr. Jung Chao Wang

Abstract

Statistical literature on testing equality of variances is very broad, encompassing a great number of distributional variations. However, the case of a zero-inflated nonnegative continuous random variable has not yet been considered. Such distribution is specified by a positive probability that the variable assumes a true zero value, together with a conditional distribution for the positive values of the variable.

This study considers the special case, delta distribution, where the positive values come from the lognormal distribution. Test procedures were developed using a statistic based on Gini's Mean Difference. Since the asymptotic distribution of the test statistic was shown to depend on parameters of the parent distribution, the new test procedures employed bootstrapping techniques (bootstrap percentile or t confidence interval). A Monte Carlo simulation study was performed to compare the proposed procedures with existing tests (classical F -test, Shoemaker's Adjusted F, Brown-Forsythe Lev:Med and Modified Fligner-Killeen F-K:Med). The new test procedures are found to be more powerful compared to existing tests.

Comments

5th Advisor: Dr. Clark D. Smothers

Access Setting

Dissertation-Open Access

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