On Reliability Estimation of Lomax Distribution under Adaptive Type-I Progressive Hybrid Censoring Scheme

Bayesian estimates involve the selection of hyper-parameters in the prior distribution. To deal with this issue, the empirical Bayesian and E-Bayesian estimates may be used to overcome this problem. The first one uses the maximum likelihood estimate (MLE) procedure to decide the hyper-parameters; wh...

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Autores principales:	Hassan Okasha, Yuhlong Lio, Mohammed Albassam
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Bayesian estimate E-Bayesian estimate empirical Bayesian Lomax distribution maximum likelihood estimate asymmetric loss function Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/ad7e1c500b83451f88e56706f0f41c2e
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spelling	oai:doaj.org-article:ad7e1c500b83451f88e56706f0f41c2e2021-11-25T18:17:03ZOn Reliability Estimation of Lomax Distribution under Adaptive Type-I Progressive Hybrid Censoring Scheme10.3390/math92229032227-7390https://doaj.org/article/ad7e1c500b83451f88e56706f0f41c2e2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2903https://doaj.org/toc/2227-7390Bayesian estimates involve the selection of hyper-parameters in the prior distribution. To deal with this issue, the empirical Bayesian and E-Bayesian estimates may be used to overcome this problem. The first one uses the maximum likelihood estimate (MLE) procedure to decide the hyper-parameters; while the second one uses the expectation of the Bayesian estimate taken over the joint prior distribution of the hyper-parameters. This study focuses on establishing the E-Bayesian estimates for the Lomax distribution shape parameter functions by utilizing the Gamma prior of the unknown shape parameter along with three distinctive joint priors of Gamma hyper-parameters based on the square error as well as two asymmetric loss functions. These two asymmetric loss functions include a general entropy and LINEX loss functions. To investigate the effect of the hyper-parameters’ selections, mathematical propositions have been derived for the E-Bayesian estimates of the three shape functions that comprise the identity, reliability and hazard rate functions. Monte Carlo simulation has been performed to compare nine E-Bayesian, three empirical Bayesian and Bayesian estimates and MLEs for any aforementioned functions. Additionally, one simulated and two real data sets from industry life test and medical study are applied for the illustrative purpose. Concluding notes are provided at the end.Hassan OkashaYuhlong LioMohammed AlbassamMDPI AGarticleBayesian estimateE-Bayesian estimateempirical BayesianLomax distributionmaximum likelihood estimateasymmetric loss functionMathematicsQA1-939ENMathematics, Vol 9, Iss 2903, p 2903 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Bayesian estimate E-Bayesian estimate empirical Bayesian Lomax distribution maximum likelihood estimate asymmetric loss function Mathematics QA1-939
spellingShingle	Bayesian estimate E-Bayesian estimate empirical Bayesian Lomax distribution maximum likelihood estimate asymmetric loss function Mathematics QA1-939 Hassan Okasha Yuhlong Lio Mohammed Albassam On Reliability Estimation of Lomax Distribution under Adaptive Type-I Progressive Hybrid Censoring Scheme
description	Bayesian estimates involve the selection of hyper-parameters in the prior distribution. To deal with this issue, the empirical Bayesian and E-Bayesian estimates may be used to overcome this problem. The first one uses the maximum likelihood estimate (MLE) procedure to decide the hyper-parameters; while the second one uses the expectation of the Bayesian estimate taken over the joint prior distribution of the hyper-parameters. This study focuses on establishing the E-Bayesian estimates for the Lomax distribution shape parameter functions by utilizing the Gamma prior of the unknown shape parameter along with three distinctive joint priors of Gamma hyper-parameters based on the square error as well as two asymmetric loss functions. These two asymmetric loss functions include a general entropy and LINEX loss functions. To investigate the effect of the hyper-parameters’ selections, mathematical propositions have been derived for the E-Bayesian estimates of the three shape functions that comprise the identity, reliability and hazard rate functions. Monte Carlo simulation has been performed to compare nine E-Bayesian, three empirical Bayesian and Bayesian estimates and MLEs for any aforementioned functions. Additionally, one simulated and two real data sets from industry life test and medical study are applied for the illustrative purpose. Concluding notes are provided at the end.
format	article
author	Hassan Okasha Yuhlong Lio Mohammed Albassam
author_facet	Hassan Okasha Yuhlong Lio Mohammed Albassam
author_sort	Hassan Okasha
title	On Reliability Estimation of Lomax Distribution under Adaptive Type-I Progressive Hybrid Censoring Scheme
title_short	On Reliability Estimation of Lomax Distribution under Adaptive Type-I Progressive Hybrid Censoring Scheme
title_full	On Reliability Estimation of Lomax Distribution under Adaptive Type-I Progressive Hybrid Censoring Scheme
title_fullStr	On Reliability Estimation of Lomax Distribution under Adaptive Type-I Progressive Hybrid Censoring Scheme
title_full_unstemmed	On Reliability Estimation of Lomax Distribution under Adaptive Type-I Progressive Hybrid Censoring Scheme
title_sort	on reliability estimation of lomax distribution under adaptive type-i progressive hybrid censoring scheme
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/ad7e1c500b83451f88e56706f0f41c2e
work_keys_str_mv	AT hassanokasha onreliabilityestimationoflomaxdistributionunderadaptivetypeiprogressivehybridcensoringscheme AT yuhlonglio onreliabilityestimationoflomaxdistributionunderadaptivetypeiprogressivehybridcensoringscheme AT mohammedalbassam onreliabilityestimationoflomaxdistributionunderadaptivetypeiprogressivehybridcensoringscheme
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On Reliability Estimation of Lomax Distribution under Adaptive Type-I Progressive Hybrid Censoring Scheme

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