Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Joshua D. Naranjo

Second Advisor

Dr. Magdalena Niewiadomska-Bugaj

Third Advisor

Dr. Jung Chao Wang

Fourth Advisor

Dr. Jezahiah Kira S. Tena


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, we 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. We investigated the performance of the classical Student's t, Welch t, and Wilcoxon-based interval 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), MLEbased 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.

Access Setting

Dissertation-Open Access