Term of Award

Summer 2013

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Department

Department of Mathematical Sciences

Committee Chair

Broderick O. Oluyede

Committee Member 1

Charles Champ

Committee Member 2

Hani Samawi

Abstract

A new class of distribution called the generalized Lindley-Weibull distribution for modeling lifetime data is proposed. This model further generalizes the Lindley distribution and allows for hazard rate functions that are monotonically decreasing, monotonically increasing bathtub and upside down bathtub shaped. The model provides a better fit to data in the sense that it leads to more accurate results and prediction, which should facilitate better public policy in a wide range of areas including but not limited to medicine and environmental health, genetics, reliability, survival analysis and time-to event data analysis. A comprehensive investigation and account of the mathematical and statistical properties and those of its sub models including estimation, and simulation issues are presented. Entropy which measures the variation of the uncertainty in a model and Fisher information are presented. Estimates of model parameters are obtained and some applications as well as numerical examples given. Estimates of sub models parameters are also determined from samples with type I right and type II doubly censored data. Real data examples are presented to illustrate the usefulness of these class of distributions.

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