Abstracts Category : Other

Transmuted families of lifetime distributions with mixture and covariates regression modelling to analyse survival data

by Muhammad Shuaib Khan

Research Doctorate - Doctor of Philosophy (PhD) This thesis develops and presents new families of transmuted lifetime distributions with covariates regression modelling for reliability and life-testing experiments. The main idea of this thesis is the quadratic rank transmutation map (QRTM) technique, used to generate a new flexible family of lifetime distributions. Chapter 1, describes the different generalised families of lifetime distributions used in this thesis. It also outlines the general framework of transmuted distributions, and provides a review of the current literature on related families of distributions. The work presented in this thesis is divided into 15 independent chapters. In chapter 2, we investigate the potential usefulness of the three parameter transmuted Weibull distribution for modelling survival data with several mathematical properties of this model. We also propose a location-scale regression model based on the log-transmuted Weibull distribution for modelling lifetime data. In chapter 3, we explore the potential usefulness of the three parameter transmuted generalised exponential distribution for analysing lifetime data. Several mathematical properties of this model are investigated. We also propose a location-scale regression model, based on the log-transmuted generalised exponential distribution. In chapter 4, we examine the transmuted Kumaraswamy (TKw) distribution. A comprehensive account of the mathematical properties of the new distribution is provided with two applications. In chapter 5, the same approach is used to study the transmuted Gompertz distribution for modelling lifetime data. Various structural properties of the transmuted Gompertz model are investigated including estimation of the parameters using maximum likelihood and evaluation of the performance of MLE using simulation. In chapter 6, we investigate the potential usefulness of the three parameter transmuted Burr type X (TBX) distribution for modelling reliability data and explore its structural properties using simulation. We also propose a location-scale regression model based on the log-TBX distribution for modelling lifetime data. In chapter 7, we introduce the three parameter transmuted Rayleigh distribution with an application to fatigue fracture data. In chapter 8, we introduce and study the transmuted Chen distribution for modelling reliability data. Various structural properties of the proposed model are derived. In chapter 9, we develop the transmuted inverse Weibull distribution with application to bladder cancer data. In chapter 10, we propose and study the transmuted exponentiated Chen distribution with two applications. We studied the important features and characteristics of the proposed model using simulation. In chapter 11, we introduce the four parameter transmuted generalized Gompertz distribution with some general statistical properties. In chapter 12, we investigate the potential usefulness of the transmuted new generalized Weibull distribution for modeling lifetime data. This distribution is anAdvisors/Committee Members: University of Newcastle. Faculty of Science, School of Mathematical and Physical Sciences.