Statistical Inferences to the Parameter and Reliability Characteristics of Gamma-mixed Rayleigh Distribution under Progressively Censored Data with Application
The purpose of the present paper is two-fold. First, we consider the estimation of the unknown model parameters and the reliability characteristics of a gamma-mixed Rayleigh distribution when a progressively type-II censored sample (PT-IICS) is available. The sufficient condition for the exis...
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Instituto Nacional de Estatística | Statistics Portugal
2025-02-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/453 |
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| author | Kousik Maiti Suchandan Kayal |
| author_facet | Kousik Maiti Suchandan Kayal |
| author_sort | Kousik Maiti |
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The purpose of the present paper is two-fold. First, we consider the estimation of the unknown model parameters and the reliability characteristics of a gamma-mixed Rayleigh distribution when a progressively type-II censored sample (PT-IICS) is available. The sufficient condition for the existence and uniqueness of the maximum likelihood estimates (MLE) is obtained. We compute MLEs using the expectation-maximization (EM) algorithm. Asymptotic confidence intervals are constructed. For comparison purposes, confidence intervals using bootstrap-p and bootstrap-t methods are also constructed. Bayes estimates are derived with respect to the squared error, LINEX, and the entropy loss functions. Two approximation techniques (Lindley and importance sampling) are used for the computation of the Bayes estimates. Further, the highest posterior density (HPD) credible intervals are derived using the importance sampling method. Second, we consider the problem of Bayesian prediction. Prediction estimates and the associated prediction equal-tail intervals under one-sample and two-sample frameworks are obtained. A simulation study is conducted the comparison the methods of estimation and prediction. Finally, a real dataset is considered and analyzed for the purpose of illustration.
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| format | Article |
| id | doaj-art-3bacd11be854456cb001c0d45fa2040f |
| institution | Kabale University |
| issn | 1645-6726 2183-0371 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj-art-3bacd11be854456cb001c0d45fa2040f2025-02-06T10:52:22ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712025-02-0123110.57805/revstat.v23i1.453Statistical Inferences to the Parameter and Reliability Characteristics of Gamma-mixed Rayleigh Distribution under Progressively Censored Data with ApplicationKousik Maiti0Suchandan Kayal 1Indian Institute of Technology RoorkeeNational Institute of Technology Rourkela The purpose of the present paper is two-fold. First, we consider the estimation of the unknown model parameters and the reliability characteristics of a gamma-mixed Rayleigh distribution when a progressively type-II censored sample (PT-IICS) is available. The sufficient condition for the existence and uniqueness of the maximum likelihood estimates (MLE) is obtained. We compute MLEs using the expectation-maximization (EM) algorithm. Asymptotic confidence intervals are constructed. For comparison purposes, confidence intervals using bootstrap-p and bootstrap-t methods are also constructed. Bayes estimates are derived with respect to the squared error, LINEX, and the entropy loss functions. Two approximation techniques (Lindley and importance sampling) are used for the computation of the Bayes estimates. Further, the highest posterior density (HPD) credible intervals are derived using the importance sampling method. Second, we consider the problem of Bayesian prediction. Prediction estimates and the associated prediction equal-tail intervals under one-sample and two-sample frameworks are obtained. A simulation study is conducted the comparison the methods of estimation and prediction. Finally, a real dataset is considered and analyzed for the purpose of illustration. https://revstat.ine.pt/index.php/REVSTAT/article/view/453Expectation-Maximization (EM) algorithmObserved Fisher information matrixBayes estimatesBayesian prediction estimatesHPD credible interval |
| spellingShingle | Kousik Maiti Suchandan Kayal Statistical Inferences to the Parameter and Reliability Characteristics of Gamma-mixed Rayleigh Distribution under Progressively Censored Data with Application Revstat Statistical Journal Expectation-Maximization (EM) algorithm Observed Fisher information matrix Bayes estimates Bayesian prediction estimates HPD credible interval |
| title | Statistical Inferences to the Parameter and Reliability Characteristics of Gamma-mixed Rayleigh Distribution under Progressively Censored Data with Application |
| title_full | Statistical Inferences to the Parameter and Reliability Characteristics of Gamma-mixed Rayleigh Distribution under Progressively Censored Data with Application |
| title_fullStr | Statistical Inferences to the Parameter and Reliability Characteristics of Gamma-mixed Rayleigh Distribution under Progressively Censored Data with Application |
| title_full_unstemmed | Statistical Inferences to the Parameter and Reliability Characteristics of Gamma-mixed Rayleigh Distribution under Progressively Censored Data with Application |
| title_short | Statistical Inferences to the Parameter and Reliability Characteristics of Gamma-mixed Rayleigh Distribution under Progressively Censored Data with Application |
| title_sort | statistical inferences to the parameter and reliability characteristics of gamma mixed rayleigh distribution under progressively censored data with application |
| topic | Expectation-Maximization (EM) algorithm Observed Fisher information matrix Bayes estimates Bayesian prediction estimates HPD credible interval |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/453 |
| work_keys_str_mv | AT kousikmaiti statisticalinferencestotheparameterandreliabilitycharacteristicsofgammamixedrayleighdistributionunderprogressivelycensoreddatawithapplication AT suchandankayal statisticalinferencestotheparameterandreliabilitycharacteristicsofgammamixedrayleighdistributionunderprogressivelycensoreddatawithapplication |