The Topp-leone generalized rayleigh distribution

Name: Pimwarat Nanthaprut

LCSH: Kasetsart University -- Dissertations. Ph.D. (Statistics) 2018

Classification :.LCCS: QA273.6

LCSH: Kasetsart University. -- Department of Statistics -- Dissertations

LCSH: Rayleigh model

LCSH: Weibull distribution

Abstract: A new three-parameter lifetime distribution called the Topp-Leone generalized Rayleigh distribution is proposed in this thesis. This distribution is obtained by the Topp-Leone generator based on the generalized Rayleigh distribution. Some mathematical properties including the survival function, hazard function, moments and moment generating function are investigated. Furthermore, the expansion of the probability density function is derived in terms of a linear combination of the generalized Rayleigh distribution, and it is utilized to obtain its moments and moment generation function. The model parameters are estimated by the maximum likelihood and Bayesian estimation. Simulation study in various scenarios is fulfilled to compare the performance of the estimators. The comparison of parameter estimators is based on the root mean square error. The simulated results show that the Bayesian method has potential to outperform the maximum likelihood method in the unimodal cases. Nevertheless, the maximum likelihood method is a better choice for the decreasing cases. In application study, the Topp-Leone generalized Rayleigh distribution is applied to three real data sets in engineering field, and also compared to the generalized Rayleigh and Rayleigh distributions. The results based on p−value of the AndersonDaring test as well as the Akaike information and Bayesian information criteria show that the Topp-Leone generalized Rayleigh distribution provides a better fit than the others. Moreover, the usefulness of the Topp-Leone generalized Rayleigh distribution is demonstrated in clinical trials application to a breast cancer data set. The result also presents that the Topp-Leone generalized Rayleigh distribution is more appropriate for fitting this data set. Therefore, we can conclude that the Topp-Leone generalized Rayleigh distribution is an alternative model to describe lifetime data.

Kasetsart University. Office of the University Library

Address: Bangkok

Email: tdckulib@ku.ac.th

Name: Mena Patummasut

Role: Thesis Advisor

Name: Winai Bodhisuwan

Role: Thesis CO-Advisor

Created: 2018

Modified: 2025-07-01

Issued: 2025-07-01

วิทยานิพนธ์/Thesis

application/pdf

URL: https://www.lib.ku.ac.th/KUthesis/2561/pimwarat-nan-all.pdf

CallNumber: QA273.6 .P56

eng

DegreeName: Doctor of Philosophy

Level: Doctoral Degree

Descipline: Statistics

Grantor: Kasetsart University

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