- Title
- Transmuted families of lifetime distributions with mixture and covariates regression modelling to analyse survival data
- Creator
- Khan, Muhammad Shuaib
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2017
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- 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 an important competitive model which contains twenty three lifetime distributions as special cases. The method of maximum likelihood is used for estimating the model parameters. In chapter 13, we introduce the transmuted Kumaraswamy (TKw) G-family for modelling life testing problems. The new extended family is obtained by using the quadratic rank transmutation map method, which possesses the bathtub shape for its hazard rate. We illustrate the potentiality of the new family with two applications to the failure and service times of Aircraft windshield data. In chapter 14, we study the transmuted Kumaraswamy Weibull distribution by using quadratic rank transmutation map technique for modelling reliability data. The proposed model contains the seventeen distributions as the special sub-models. We also propose a location-scale regression model based on the transmuted log-Kumaraswamy Weibull distribution for modelling survival data. We discuss estimation of the model parameters by the method of maximum likelihood and provide two applications to illustrate the potentiality of the transmuted Kumaraswamy Weibull family of lifetime distributions. Chapter 15 comprises the conclusions and suggestions for future work.
- Subject
- transmuted Kumaraswamy Burr XII distribution; transmuted Kumaraswamy Weibull distribution; moments; order statistics; maximum likelihood estimation; thesis by publication
- Identifier
- http://hdl.handle.net/1959.13/1347457
- Identifier
- uon:30046
- Rights
- Copyright 2017 Muhammad Shuaib Khan
- Language
- eng
- Full Text
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| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Thesis | 3 MB | Adobe Acrobat PDF | View Details Download | ||
| View Details Download | ATTACHMENT02 | Abstract | 219 KB | Adobe Acrobat PDF | View Details Download |