A 3-Component Mixture of Rayleigh Distributions: Properties and Estimation in Bayesian Framework

To study lifetimes of certain engineering processes, a lifetime model which can accommodate the nature of such processes is desired. The mixture models of underlying lifetime distributions are intuitively more appropriate and appealing to model the heterogeneous nature of process as compared to simp...

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Main Authors:	Aslam, Muhammad, Tahir, Muhammad, Hussain, Zawar, Al-Zahrani, Bander
Format:	Online
Language:	English
Published:	Public Library of Science 2015
Online Access:	https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4439070/

id	pubmed-4439070
recordtype	oai_dc
spelling	pubmed-44390702015-05-29 A 3-Component Mixture of Rayleigh Distributions: Properties and Estimation in Bayesian Framework Aslam, Muhammad Tahir, Muhammad Hussain, Zawar Al-Zahrani, Bander Research Article To study lifetimes of certain engineering processes, a lifetime model which can accommodate the nature of such processes is desired. The mixture models of underlying lifetime distributions are intuitively more appropriate and appealing to model the heterogeneous nature of process as compared to simple models. This paper is about studying a 3-component mixture of the Rayleigh distributionsin Bayesian perspective. The censored sampling environment is considered due to its popularity in reliability theory and survival analysis. The expressions for the Bayes estimators and their posterior risks are derived under different scenarios. In case the case that no or little prior information is available, elicitation of hyperparameters is given. To examine, numerically, the performance of the Bayes estimators using non-informative and informative priors under different loss functions, we have simulated their statistical properties for different sample sizes and test termination times. In addition, to highlight the practical significance, an illustrative example based on a real-life engineering data is also given. Public Library of Science 2015-05-20 /pmc/articles/PMC4439070/ /pubmed/25993475 http://dx.doi.org/10.1371/journal.pone.0126183 Text en © 2015 Aslam et al http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
repository_type	Open Access Journal
institution_category	Foreign Institution
institution	US National Center for Biotechnology Information
building	NCBI PubMed
collection	Online Access
language	English
format	Online
author	Aslam, Muhammad Tahir, Muhammad Hussain, Zawar Al-Zahrani, Bander
spellingShingle	Aslam, Muhammad Tahir, Muhammad Hussain, Zawar Al-Zahrani, Bander A 3-Component Mixture of Rayleigh Distributions: Properties and Estimation in Bayesian Framework
author_facet	Aslam, Muhammad Tahir, Muhammad Hussain, Zawar Al-Zahrani, Bander
author_sort	Aslam, Muhammad
title	A 3-Component Mixture of Rayleigh Distributions: Properties and Estimation in Bayesian Framework
title_short	A 3-Component Mixture of Rayleigh Distributions: Properties and Estimation in Bayesian Framework
title_full	A 3-Component Mixture of Rayleigh Distributions: Properties and Estimation in Bayesian Framework
title_fullStr	A 3-Component Mixture of Rayleigh Distributions: Properties and Estimation in Bayesian Framework
title_full_unstemmed	A 3-Component Mixture of Rayleigh Distributions: Properties and Estimation in Bayesian Framework
title_sort	3-component mixture of rayleigh distributions: properties and estimation in bayesian framework
description	To study lifetimes of certain engineering processes, a lifetime model which can accommodate the nature of such processes is desired. The mixture models of underlying lifetime distributions are intuitively more appropriate and appealing to model the heterogeneous nature of process as compared to simple models. This paper is about studying a 3-component mixture of the Rayleigh distributionsin Bayesian perspective. The censored sampling environment is considered due to its popularity in reliability theory and survival analysis. The expressions for the Bayes estimators and their posterior risks are derived under different scenarios. In case the case that no or little prior information is available, elicitation of hyperparameters is given. To examine, numerically, the performance of the Bayes estimators using non-informative and informative priors under different loss functions, we have simulated their statistical properties for different sample sizes and test termination times. In addition, to highlight the practical significance, an illustrative example based on a real-life engineering data is also given.
publisher	Public Library of Science
publishDate	2015
url	https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4439070/
_version_	1613226142048714752

A 3-Component Mixture of Rayleigh Distributions: Properties and Estimation in Bayesian Framework

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