Dissertation Defenses

Doctoral Dissertation Announcement

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Candidate: Jezaniah Kira Sarion Tena

Degree of: Doctor of Philosophy

Department: Statistics

Title: Test Procedures for Equality of Two Variances in Delta Distributions

Committee:
Dr. Magdalena Niewiadomska-Bugaj, Chair
Dr. Joshua D. Naranjo
Dr. Gerald L. Sievers
Dr. Jung Chao Wang
Dr. Clark D. Smothers

Date: Tuesday, April 28, 2009 10:00 a.m. - 12:00 p.m.
6625 Everett Tower

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 non-negative 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 are developed using a statistic based on Gini’s Mean Difference. Since the asymptotic distribution of the test statistic is shown to depend on parameters of the parent distribution, the new test procedures employ bootstrapping techniques (bootstrap percentile or t confidence interval). A Monte Carlo simulation study is 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.