Date of Award

5-2015

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Mavis Pararai, Ph.D.

Second Advisor

Christoph E. Maier, Ph.D.

Third Advisor

Russell S. Stocker, Ph.D.

Fourth Advisor

Yongtao Cao, Ph.D.

Abstract

The aim of this thesis is to propose a new class of lifetime distributions called the Lindley power series (LPS). The distribution properties including survival function, hazard and reverse hazard functions, limiting behavior of the pdf and hazard function, quantile function, moments, distribution of order statistics, mean deviations, Lorenz and Bonferroni curves and Fisher information are presented. The method of maximum likelihood estimation is used to estimate the model parameters of this new class of distributions. The special cases of the LPS distribution including Lindley binomial (LB), Lindley geometric (LG), Lindley Poisson (LP) and Lindley logarithmic (LL) distributions are presented. The Lindley logarithmic (LL) distribution is discussed in detail. A Monte Carlo simulation study is presented to exhibit the performance and accuracy of maximum likelihood estimates of the LL model parameters. Some real data examples are discussed to illustrate the usefulness and applicability of the LL distribution.

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