Generalized Fiducial Inference for the Stress–Strength Reliability of Generalized Logistic Distribution
Generalized logistic distribution, as the generalized form of the symmetric logistic distribution, plays an important role in reliability analysis. This article focuses on the statistical inference for the stress–strength parameter <inline-formula><math xmlns="http://www.w3.org/1998/Ma...
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MDPI AG
2023-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/7/1365 |
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| author | Menghan Li Liang Yan Yaru Qiao Xia Cai Khamis K. Said |
| author_facet | Menghan Li Liang Yan Yaru Qiao Xia Cai Khamis K. Said |
| author_sort | Menghan Li |
| collection | DOAJ |
| description | Generalized logistic distribution, as the generalized form of the symmetric logistic distribution, plays an important role in reliability analysis. This article focuses on the statistical inference for the stress–strength parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>Y</mi><mo><</mo><mi>X</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> of the generalized logistic distribution with the same and different scale parameters. Firstly, we use the frequentist method to construct asymptotic confidence intervals, and adopt the generalized inference method for constructing the generalized point estimators as well as the generalized confidence intervals. Then the generalized fiducial method is applied to construct the fiducial point estimators and the fiducial confidence intervals. Simulation results demonstrate that the generalized fiducial method outperforms other methods in terms of the mean square error, average length, and empirical coverage. Finally, three real datasets are used to illustrate the proposed methods. |
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| format | Article |
| id | doaj.art-f4f466f6feaf4bdcb8e466c187cd3804 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T00:36:42Z |
| publishDate | 2023-07-01 |
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| series | Symmetry |
| spelling | doaj.art-f4f466f6feaf4bdcb8e466c187cd38042023-11-18T21:34:03ZengMDPI AGSymmetry2073-89942023-07-01157136510.3390/sym15071365Generalized Fiducial Inference for the Stress–Strength Reliability of Generalized Logistic DistributionMenghan Li0Liang Yan1Yaru Qiao2Xia Cai3Khamis K. Said4School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, ChinaSchool of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, ChinaSchool of Science, Hebei University of Science and Technology, Shijiazhuang 050018, ChinaSchool of Science, Hebei University of Science and Technology, Shijiazhuang 050018, ChinaDepartment of Science, Karume Institute of Science and Technology, Zanzibar P.O. Box 467, TanzaniaGeneralized logistic distribution, as the generalized form of the symmetric logistic distribution, plays an important role in reliability analysis. This article focuses on the statistical inference for the stress–strength parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>Y</mi><mo><</mo><mi>X</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> of the generalized logistic distribution with the same and different scale parameters. Firstly, we use the frequentist method to construct asymptotic confidence intervals, and adopt the generalized inference method for constructing the generalized point estimators as well as the generalized confidence intervals. Then the generalized fiducial method is applied to construct the fiducial point estimators and the fiducial confidence intervals. Simulation results demonstrate that the generalized fiducial method outperforms other methods in terms of the mean square error, average length, and empirical coverage. Finally, three real datasets are used to illustrate the proposed methods.https://www.mdpi.com/2073-8994/15/7/1365generalized fiducial inferencestress–strengthgeneralized logistic distributionpoint estimationinterval estimation |
| spellingShingle | Menghan Li Liang Yan Yaru Qiao Xia Cai Khamis K. Said Generalized Fiducial Inference for the Stress–Strength Reliability of Generalized Logistic Distribution Symmetry generalized fiducial inference stress–strength generalized logistic distribution point estimation interval estimation |
| title | Generalized Fiducial Inference for the Stress–Strength Reliability of Generalized Logistic Distribution |
| title_full | Generalized Fiducial Inference for the Stress–Strength Reliability of Generalized Logistic Distribution |
| title_fullStr | Generalized Fiducial Inference for the Stress–Strength Reliability of Generalized Logistic Distribution |
| title_full_unstemmed | Generalized Fiducial Inference for the Stress–Strength Reliability of Generalized Logistic Distribution |
| title_short | Generalized Fiducial Inference for the Stress–Strength Reliability of Generalized Logistic Distribution |
| title_sort | generalized fiducial inference for the stress strength reliability of generalized logistic distribution |
| topic | generalized fiducial inference stress–strength generalized logistic distribution point estimation interval estimation |
| url | https://www.mdpi.com/2073-8994/15/7/1365 |
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