Bayesian Inference and Data Analysis of the Unit–Power Burr X Distribution
The unit–power Burr X distribution (UPBXD), a bounded version of the power Burr X distribution, is presented. The UPBXD is produced through the inverse exponential transformation of the power Burr X distribution, which is also beneficial for modelling data on the unit interval. Comprehensive analysi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/3/297 |
| _version_ | 1797613524478853120 |
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| author | Aisha Fayomi Amal S. Hassan Hanan Baaqeel Ehab M. Almetwally |
| author_facet | Aisha Fayomi Amal S. Hassan Hanan Baaqeel Ehab M. Almetwally |
| author_sort | Aisha Fayomi |
| collection | DOAJ |
| description | The unit–power Burr X distribution (UPBXD), a bounded version of the power Burr X distribution, is presented. The UPBXD is produced through the inverse exponential transformation of the power Burr X distribution, which is also beneficial for modelling data on the unit interval. Comprehensive analysis of its key characteristics is performed, including shape analysis of the primary functions, analytical expression for moments, quantile function, incomplete moments, stochastic ordering, and stress–strength reliability. Rényi, Havrda and Charvat, and d-generalized entropies, which are measures of uncertainty, are also obtained. The model’s parameters are estimated using a Bayesian estimation approach via symmetric and asymmetric loss functions. The Bayesian credible intervals are constructed based on the marginal posterior distribution. Monte Carlo simulation research is intended to test the accuracy of various estimators based on certain measures, in accordance with the complex forms of Bayesian estimators. Finally, we show that the new distribution is more appropriate than certain other competing models, according to their application for COVID-19 in Saudi Arabia and the United Kingdom. |
| first_indexed | 2024-03-11T06:56:57Z |
| format | Article |
| id | doaj.art-e92a6242aa67442cbbf68728e37e180c |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T06:56:57Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-e92a6242aa67442cbbf68728e37e180c2023-11-17T09:35:32ZengMDPI AGAxioms2075-16802023-03-0112329710.3390/axioms12030297Bayesian Inference and Data Analysis of the Unit–Power Burr X DistributionAisha Fayomi0Amal S. Hassan1Hanan Baaqeel2Ehab M. Almetwally3Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaFaculty of Graduate Studies for Statistical Research (FGSSR), Cairo University, Giza 12613, EgyptDepartment of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaFaculty of Business Administration, Delta University for Science and Technology, Gamasa 11152, EgyptThe unit–power Burr X distribution (UPBXD), a bounded version of the power Burr X distribution, is presented. The UPBXD is produced through the inverse exponential transformation of the power Burr X distribution, which is also beneficial for modelling data on the unit interval. Comprehensive analysis of its key characteristics is performed, including shape analysis of the primary functions, analytical expression for moments, quantile function, incomplete moments, stochastic ordering, and stress–strength reliability. Rényi, Havrda and Charvat, and d-generalized entropies, which are measures of uncertainty, are also obtained. The model’s parameters are estimated using a Bayesian estimation approach via symmetric and asymmetric loss functions. The Bayesian credible intervals are constructed based on the marginal posterior distribution. Monte Carlo simulation research is intended to test the accuracy of various estimators based on certain measures, in accordance with the complex forms of Bayesian estimators. Finally, we show that the new distribution is more appropriate than certain other competing models, according to their application for COVID-19 in Saudi Arabia and the United Kingdom.https://www.mdpi.com/2075-1680/12/3/297power Burr X distributionentropyBayesian estimationMetropolis–HastingsCOVID-19 data |
| spellingShingle | Aisha Fayomi Amal S. Hassan Hanan Baaqeel Ehab M. Almetwally Bayesian Inference and Data Analysis of the Unit–Power Burr X Distribution Axioms power Burr X distribution entropy Bayesian estimation Metropolis–Hastings COVID-19 data |
| title | Bayesian Inference and Data Analysis of the Unit–Power Burr X Distribution |
| title_full | Bayesian Inference and Data Analysis of the Unit–Power Burr X Distribution |
| title_fullStr | Bayesian Inference and Data Analysis of the Unit–Power Burr X Distribution |
| title_full_unstemmed | Bayesian Inference and Data Analysis of the Unit–Power Burr X Distribution |
| title_short | Bayesian Inference and Data Analysis of the Unit–Power Burr X Distribution |
| title_sort | bayesian inference and data analysis of the unit power burr x distribution |
| topic | power Burr X distribution entropy Bayesian estimation Metropolis–Hastings COVID-19 data |
| url | https://www.mdpi.com/2075-1680/12/3/297 |
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