Karen Grace Villarente Rosales

Doctoral Dissertation Announcement

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Candidate: Karen Grace Villarente Rosales

Degree of: Doctor of Philosophy

Department: Statistics

Title: Confidence Intervals and Tests on the Difference of Means of Two Delta Distributions

Committee:
Dr. Joshua Naranjo, Chair
Dr. Magdalena Niewiadomska-Bugaj
Dr. Jung-Chao Wang
Dr. Jezaniah Kira Tena

Date: Friday, November 12, 2010 10:30 a.m. to 12:30 p.m.
6625 Everett Tower

Abstract:
Various research fields produce data that are lognormally distributed and inflated with zero values. This type of data follows a delta distribution. In this study, the researchers want to extensively investigate different interval and hypothesis testing methods for comparing the means of two delta populations to see which methods are optimal under different conditions of the populations.
For confidence intervals, existing MVUE methods are extended to two sample cases and compared to classical and two proposed robust methods. The performance of the classical Student's t, Welch t, and Wilcoxon-based interval is investigated to see if these methods really perform badly on zero-inflated data. A simulation study is done to assess coverage accuracy of all the methods. Hypothesis testing on the equality of means of two delta distributions is done using confidence intervals. The previous interval methods are compared with two-part models by Lachenbruch (2001), MLE-based intervals, and two proposed robust intervals. The performance of the tests are assessed through a simulation study where the Type I error rates and power rates are computed. A robustness study is conducted by comparing the performance of estimators and tests under various distributions like gamma and Weibull.
Additionally, the Wilcoxon-based interval is assessed on three parameters that measure the difference of the two delta distributions namely, difference of means, difference of medians and median of differences. A simulation study is conducted to evaluate the performance of the three parameters of differences. The Wilcoxon-based interval was found to measure the median of differences best.