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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| Format: | Article |
| Language: | English |
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University of Baghdad, College of Science for Women
2023-06-01
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| 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 |
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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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| format | Article |
| id | doaj-art-bfb1c1c057e94bff9e6e36d4f3b83a7b |
| 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 |