Comparison of the Bayesian and maximum likelilhood estimation for Weibull distribution

Problem statement: The Weibull distribution has been widely used especially in the modeling of lifetime event data. It provides a statistical model which has a wide variety of applications in many areas, and the main advantage is its ability in the context of lifetime event, to provide reasonably...

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Main Authors:	Al Omari, Mohammed Ahmed, Al-Kutubi, Hadeel Salim, Ibrahim, Noor Akma
Format:	Article
Language:	English
Published:	Science Publications 2010
Online Access:	http://psasir.upm.edu.my/id/eprint/13705/ http://psasir.upm.edu.my/id/eprint/13705/ http://psasir.upm.edu.my/id/eprint/13705/ http://psasir.upm.edu.my/id/eprint/13705/1/Comparison%20of%20the%20Bayesian%20and%20maximum%20likelilhood%20estimation%20for%20Weibull%20distribution.pdf

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recordtype	eprints
spelling	upm-137052015-10-23T02:36:43Z http://psasir.upm.edu.my/id/eprint/13705/ Comparison of the Bayesian and maximum likelilhood estimation for Weibull distribution Al Omari, Mohammed Ahmed Al-Kutubi, Hadeel Salim Ibrahim, Noor Akma Problem statement: The Weibull distribution has been widely used especially in the modeling of lifetime event data. It provides a statistical model which has a wide variety of applications in many areas, and the main advantage is its ability in the context of lifetime event, to provide reasonably accurate failure analysis and failure for ecasts especially with extremely small samples. The conventional maximum likelihood method is the usual way to estimate the parameters of a distribution. Bayesian approach has received much attention and in contention with other estimation methods. In this study we explore and compare the performance of the maximum likelihood estimate with the Bayesian estimate for the Weibull distribution. Approach: The maximum likelihood estimation, Bayesian using Jeffrey prior and the extension of Jeffrey prior information for estimating the parameters of Weibull distribution of life time are presented. We explore the performance of these estimators numerically under varyin g conditions. Through the simulation study comparison are made on the performance of these estimators with respect to the Mean Square Error (MSE) and Mean Percentage Error(MPE). Results: For all the varying sample size, several specific values of the scale parameter of the Weibull distribution and for the values specify for the extension of Jeffrey prior, the estimators of the maximum likelihood method result in smaller MSE and MPE compared to Bayesian in majority of the cases. Nevertheless in all cases for both methods the MSE and MPE decrease as sample size increases. Conclusion: Based on the results of this simulation study the Bayesian approach used in the estimating of Weibull parameters is found to be not superior compared to the conventional maximum likelihood method with respect to MSE and MPE values. Science Publications 2010-06-30 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/13705/1/Comparison%20of%20the%20Bayesian%20and%20maximum%20likelilhood%20estimation%20for%20Weibull%20distribution.pdf Al Omari, Mohammed Ahmed and Al-Kutubi, Hadeel Salim and Ibrahim, Noor Akma (2010) Comparison of the Bayesian and maximum likelilhood estimation for Weibull distribution. Journal of Mathematics and Statistics, 6 (2). pp. 100-104. ISSN 1549-3644; ESSN: 1558-6359 http://www.thescipub.com/abstract/10.3844/jmssp.2010.100.104 10.3844/jmssp.2010.100.104
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Putra Malaysia
building	UPM Institutional Repository
collection	Online Access
language	English
description	Problem statement: The Weibull distribution has been widely used especially in the modeling of lifetime event data. It provides a statistical model which has a wide variety of applications in many areas, and the main advantage is its ability in the context of lifetime event, to provide reasonably accurate failure analysis and failure for ecasts especially with extremely small samples. The conventional maximum likelihood method is the usual way to estimate the parameters of a distribution. Bayesian approach has received much attention and in contention with other estimation methods. In this study we explore and compare the performance of the maximum likelihood estimate with the Bayesian estimate for the Weibull distribution. Approach: The maximum likelihood estimation, Bayesian using Jeffrey prior and the extension of Jeffrey prior information for estimating the parameters of Weibull distribution of life time are presented. We explore the performance of these estimators numerically under varyin g conditions. Through the simulation study comparison are made on the performance of these estimators with respect to the Mean Square Error (MSE) and Mean Percentage Error(MPE). Results: For all the varying sample size, several specific values of the scale parameter of the Weibull distribution and for the values specify for the extension of Jeffrey prior, the estimators of the maximum likelihood method result in smaller MSE and MPE compared to Bayesian in majority of the cases. Nevertheless in all cases for both methods the MSE and MPE decrease as sample size increases. Conclusion: Based on the results of this simulation study the Bayesian approach used in the estimating of Weibull parameters is found to be not superior compared to the conventional maximum likelihood method with respect to MSE and MPE values.
format	Article
author	Al Omari, Mohammed Ahmed Al-Kutubi, Hadeel Salim Ibrahim, Noor Akma
spellingShingle	Al Omari, Mohammed Ahmed Al-Kutubi, Hadeel Salim Ibrahim, Noor Akma Comparison of the Bayesian and maximum likelilhood estimation for Weibull distribution
author_facet	Al Omari, Mohammed Ahmed Al-Kutubi, Hadeel Salim Ibrahim, Noor Akma
author_sort	Al Omari, Mohammed Ahmed
title	Comparison of the Bayesian and maximum likelilhood estimation for Weibull distribution
title_short	Comparison of the Bayesian and maximum likelilhood estimation for Weibull distribution
title_full	Comparison of the Bayesian and maximum likelilhood estimation for Weibull distribution
title_fullStr	Comparison of the Bayesian and maximum likelilhood estimation for Weibull distribution
title_full_unstemmed	Comparison of the Bayesian and maximum likelilhood estimation for Weibull distribution
title_sort	comparison of the bayesian and maximum likelilhood estimation for weibull distribution
publisher	Science Publications
publishDate	2010
url	http://psasir.upm.edu.my/id/eprint/13705/ http://psasir.upm.edu.my/id/eprint/13705/ http://psasir.upm.edu.my/id/eprint/13705/ http://psasir.upm.edu.my/id/eprint/13705/1/Comparison%20of%20the%20Bayesian%20and%20maximum%20likelilhood%20estimation%20for%20Weibull%20distribution.pdf
first_indexed	2018-09-07T13:25:34Z
last_indexed	2018-09-07T13:25:34Z
_version_	1610955342584217600

Comparison of the Bayesian and maximum likelilhood estimation for Weibull distribution

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