Author

Hongbo Yu

Graduation Semester and Year

2017

Language

English

Document Type

Thesis

Degree Name

Master of Science in Mathematics

Department

Mathematics

First Advisor

Suvra Pal

Abstract

In this study, we have considered analysis of lifetime or survival data with right censoring, which is the most common form of censoring encountered in practice. Assuming a fully parametric setup, the main objective is to consider a wider family of distributions for the lifetime and then find the maximum likelihood estimates of the model parameters using some optimization technique available in R statistical software. In this work, the generalized gamma distribution is considered as the distribution for the lifetime which is flexible in the sense that it contains some of the commonly used lifetime distributions, such as Weibull, gamma, and lognormal, as its special case. This flexibility allows us to carry out a formal test of hypothesis to determine a particular distribution within this family that provides an adequate fit to the data. Another objective is to carry out an extensive Monte Carlo simulation study to demonstrate the performance of the estimation method and the flexibility of the generalized gamma family. To demonstrate the flexibility of the generalized gamma family, we carried out a model discrimination using the likelihood ratio test and information-based criteria. Finally, we illustrate the estimation method and the flexibility of the generalized gamma family using a real data.

Keywords

Generalized gamma distribution, Parameter estimation, Model discrimination

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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