Estimation of Parameters for the Gumbel Type-I Distribution under Type-II Censoring Scheme

This paper aims to decide the best parameter estimation methods for the parameters of the Gumbel type-I distribution under the type-II censorship scheme. For this purpose, classical and Bayesian parameter estimation procedures are considered. The maximum likelihood estimators are used for the class...

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Main Authors: Asuman Yılmaz, Mahmut Kara
Format: Article
Language:English
Published: University of Baghdad, College of Science for Women 2023-06-01
Series:مجلة بغداد للعلوم
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Online Access:https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/6898
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author Asuman Yılmaz
Mahmut Kara
author_facet Asuman Yılmaz
Mahmut Kara
author_sort Asuman Yılmaz
collection DOAJ
description This paper aims to decide the best parameter estimation methods for the parameters of the Gumbel type-I distribution under the type-II censorship scheme. For this purpose, classical and Bayesian parameter estimation procedures are considered. The maximum likelihood estimators are used for the classical parameter estimation procedure. The asymptotic distributions of these estimators are also derived. It is not possible to obtain explicit solutions of Bayesian estimators. Therefore, Markov Chain Monte Carlo, and Lindley techniques are taken into account to estimate the unknown parameters. In Bayesian analysis, it is very important to determine an appropriate combination of a prior distribution and a loss function. Therefore, two different prior distributions are used. Also, the Bayesian estimators concerning the parameters of interest under various loss functions are investigated. The Gibbs sampling algorithm is used to construct the Bayesian credible intervals. Then, the efficiencies of the maximum likelihood estimators are compared with Bayesian estimators via an extensive Monte Carlo simulation study. It has been shown that the Bayesian estimators are considerably more efficient than the maximum likelihood estimators. Finally, a real-life example is also presented for application purposes.
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institution Kabale University
issn 2078-8665
2411-7986
language English
publishDate 2023-06-01
publisher University of Baghdad, College of Science for Women
record_format Article
series مجلة بغداد للعلوم
spelling doaj-art-bfb1c1c057e94bff9e6e36d4f3b83a7b2025-08-20T03:39:04ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862023-06-0120310.21123/bsj.2022.6898Estimation of Parameters for the Gumbel Type-I Distribution under Type-II Censoring SchemeAsuman Yılmaz0Mahmut Kara1Department of Econometrics, Faculty of Economics and Administrative Sciences, Van Yüzüncü Yıl University, 65080 Van, Turkey.Department of Econometrics, Faculty of Economics and Administrative Sciences, Van Yüzüncü Yıl University, 65080 Van, Turkey. This paper aims to decide the best parameter estimation methods for the parameters of the Gumbel type-I distribution under the type-II censorship scheme. For this purpose, classical and Bayesian parameter estimation procedures are considered. The maximum likelihood estimators are used for the classical parameter estimation procedure. The asymptotic distributions of these estimators are also derived. It is not possible to obtain explicit solutions of Bayesian estimators. Therefore, Markov Chain Monte Carlo, and Lindley techniques are taken into account to estimate the unknown parameters. In Bayesian analysis, it is very important to determine an appropriate combination of a prior distribution and a loss function. Therefore, two different prior distributions are used. Also, the Bayesian estimators concerning the parameters of interest under various loss functions are investigated. The Gibbs sampling algorithm is used to construct the Bayesian credible intervals. Then, the efficiencies of the maximum likelihood estimators are compared with Bayesian estimators via an extensive Monte Carlo simulation study. It has been shown that the Bayesian estimators are considerably more efficient than the maximum likelihood estimators. Finally, a real-life example is also presented for application purposes. https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/6898Bayesian Methods, Gumbel Type-I Distribution, Simulation, Type -II Censoring
spellingShingle Asuman Yılmaz
Mahmut Kara
Estimation of Parameters for the Gumbel Type-I Distribution under Type-II Censoring Scheme
مجلة بغداد للعلوم
Bayesian Methods, Gumbel Type-I Distribution, Simulation, Type -II Censoring
title Estimation of Parameters for the Gumbel Type-I Distribution under Type-II Censoring Scheme
title_full Estimation of Parameters for the Gumbel Type-I Distribution under Type-II Censoring Scheme
title_fullStr Estimation of Parameters for the Gumbel Type-I Distribution under Type-II Censoring Scheme
title_full_unstemmed Estimation of Parameters for the Gumbel Type-I Distribution under Type-II Censoring Scheme
title_short Estimation of Parameters for the Gumbel Type-I Distribution under Type-II Censoring Scheme
title_sort estimation of parameters for the gumbel type i distribution under type ii censoring scheme
topic Bayesian Methods, Gumbel Type-I Distribution, Simulation, Type -II Censoring
url https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/6898
work_keys_str_mv AT asumanyılmaz estimationofparametersforthegumbeltypeidistributionundertypeiicensoringscheme
AT mahmutkara estimationofparametersforthegumbeltypeidistributionundertypeiicensoringscheme