Parameter estimations and copula methods for burr type III and type XII distributions

Continuous Burr distributions have gained popularity recently due to their potential use in practical situations. In particular, Burr Type III and Type XII distributions are suitable to describe lifetime data since these distributions, not only have flexible shape but also controllable scale and loc...

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Main Author:	Ismail, Nor Hidayah
Format:	Thesis
Language:	English
Published:	2014
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/77979/1/NorHidayahIsmailMFS20141.pdf
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spelling	my-utm-ep.779792018-07-18T07:38:35Z Parameter estimations and copula methods for burr type III and type XII distributions 2014-12 Ismail, Nor Hidayah QA Mathematics Continuous Burr distributions have gained popularity recently due to their potential use in practical situations. In particular, Burr Type III and Type XII distributions are suitable to describe lifetime data since these distributions, not only have flexible shape but also controllable scale and location parameters which are needed in characterizing lifetime distributions. In this study, 2-parameter and 3-parameter Burr Type III and XII distributions are employed to fit a set of simulated lifetime data. These lifetime data are assumed to be either complete, that is uncensored, or censored at varying levels of censoring, and are simulated from the specified Burr distributions using their inverse cumulative distribution functions. The distribution parameters are then estimated by using the classical maximum likelihood estimation (MLE) and expectation-maximization (EM) algorithm approaches. The performance of parameter estimates are then compared in terms of their accuracy and efficiency by comparing its bias and mean square errors. The study finds that as the censoring level varies, the EM estimates perform better than the MLE estimates for 2-parameter and 3-parameter Burr Type III and XII distributions with complete and censored lifetime data at certain censoring levels. In addition, the study also investigates a number of copula methods to join specific Burr Type III and XII distributions. The result reveals that Ali-Mikhail-Haq, Clayton and Gumbel methods fit well with Burr distributions for uncensored lifetime data since the values of copula lie within (0,1) interval. 2014-12 Thesis http://eprints.utm.my/id/eprint/77979/ http://eprints.utm.my/id/eprint/77979/1/NorHidayahIsmailMFS20141.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:86002 masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Ismail, Nor Hidayah Parameter estimations and copula methods for burr type III and type XII distributions
description	Continuous Burr distributions have gained popularity recently due to their potential use in practical situations. In particular, Burr Type III and Type XII distributions are suitable to describe lifetime data since these distributions, not only have flexible shape but also controllable scale and location parameters which are needed in characterizing lifetime distributions. In this study, 2-parameter and 3-parameter Burr Type III and XII distributions are employed to fit a set of simulated lifetime data. These lifetime data are assumed to be either complete, that is uncensored, or censored at varying levels of censoring, and are simulated from the specified Burr distributions using their inverse cumulative distribution functions. The distribution parameters are then estimated by using the classical maximum likelihood estimation (MLE) and expectation-maximization (EM) algorithm approaches. The performance of parameter estimates are then compared in terms of their accuracy and efficiency by comparing its bias and mean square errors. The study finds that as the censoring level varies, the EM estimates perform better than the MLE estimates for 2-parameter and 3-parameter Burr Type III and XII distributions with complete and censored lifetime data at certain censoring levels. In addition, the study also investigates a number of copula methods to join specific Burr Type III and XII distributions. The result reveals that Ali-Mikhail-Haq, Clayton and Gumbel methods fit well with Burr distributions for uncensored lifetime data since the values of copula lie within (0,1) interval.
format	Thesis
qualification_level	Master's degree
author	Ismail, Nor Hidayah
author_facet	Ismail, Nor Hidayah
author_sort	Ismail, Nor Hidayah
title	Parameter estimations and copula methods for burr type III and type XII distributions
title_short	Parameter estimations and copula methods for burr type III and type XII distributions
title_full	Parameter estimations and copula methods for burr type III and type XII distributions
title_fullStr	Parameter estimations and copula methods for burr type III and type XII distributions
title_full_unstemmed	Parameter estimations and copula methods for burr type III and type XII distributions
title_sort	parameter estimations and copula methods for burr type iii and type xii distributions
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2014
url	http://eprints.utm.my/id/eprint/77979/1/NorHidayahIsmailMFS20141.pdf
_version_	1747817877671510016

Parameter estimations and copula methods for burr type III and type XII distributions

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