Bivariate Power Lindley Models Based on Copula Functions Under Type-II Censored Samples With Applications in Industrial and Medical Data
This study introduces three innovative bivariate models to address complex dependencies between random variables in real-world applications. Specifically, we develop bivariate power Lindley (BPL) distribution models utilizing the Gumbel, Frank, and Clayton copulas. These models effectively capture t...
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/jom/5904687 |
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| _version_ | 1849427870675369984 |
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| author | Ehab M. Almetwally Aisha Fayomi Maha E. Qura |
| author_facet | Ehab M. Almetwally Aisha Fayomi Maha E. Qura |
| author_sort | Ehab M. Almetwally |
| collection | DOAJ |
| description | This study introduces three innovative bivariate models to address complex dependencies between random variables in real-world applications. Specifically, we develop bivariate power Lindley (BPL) distribution models utilizing the Gumbel, Frank, and Clayton copulas. These models effectively capture the underlying relationships between variables, particularly under a Type-II censored sampling scheme. Parameter estimation is performed using both maximum likelihood and Bayesian methods, with asymptotic and credible confidence intervals computed. We also employ the Markov Chain Monte Carlo method for numerical analysis. The proposed methodology is demonstrated through the analysis of multiple datasets: the first investigates burr formation in manufacturing with two sets of observations, while the second and third datasets explore medical data on diabetic nephropathy and infection recurrence times in kidney patients, respectively. The results highlight the practical applicability and robustness of these newly proposed bivariate models. |
| format | Article |
| id | doaj-art-35dd2f4f236f4d66b0bdc41d93eac834 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-35dd2f4f236f4d66b0bdc41d93eac8342025-08-20T03:28:53ZengWileyJournal of Mathematics2314-47852025-01-01202510.1155/jom/5904687Bivariate Power Lindley Models Based on Copula Functions Under Type-II Censored Samples With Applications in Industrial and Medical DataEhab M. Almetwally0Aisha Fayomi1Maha E. Qura2Department of Mathematics and StatisticsDepartment of StatisticsDepartment of StatisticsThis study introduces three innovative bivariate models to address complex dependencies between random variables in real-world applications. Specifically, we develop bivariate power Lindley (BPL) distribution models utilizing the Gumbel, Frank, and Clayton copulas. These models effectively capture the underlying relationships between variables, particularly under a Type-II censored sampling scheme. Parameter estimation is performed using both maximum likelihood and Bayesian methods, with asymptotic and credible confidence intervals computed. We also employ the Markov Chain Monte Carlo method for numerical analysis. The proposed methodology is demonstrated through the analysis of multiple datasets: the first investigates burr formation in manufacturing with two sets of observations, while the second and third datasets explore medical data on diabetic nephropathy and infection recurrence times in kidney patients, respectively. The results highlight the practical applicability and robustness of these newly proposed bivariate models.http://dx.doi.org/10.1155/jom/5904687 |
| spellingShingle | Ehab M. Almetwally Aisha Fayomi Maha E. Qura Bivariate Power Lindley Models Based on Copula Functions Under Type-II Censored Samples With Applications in Industrial and Medical Data Journal of Mathematics |
| title | Bivariate Power Lindley Models Based on Copula Functions Under Type-II Censored Samples With Applications in Industrial and Medical Data |
| title_full | Bivariate Power Lindley Models Based on Copula Functions Under Type-II Censored Samples With Applications in Industrial and Medical Data |
| title_fullStr | Bivariate Power Lindley Models Based on Copula Functions Under Type-II Censored Samples With Applications in Industrial and Medical Data |
| title_full_unstemmed | Bivariate Power Lindley Models Based on Copula Functions Under Type-II Censored Samples With Applications in Industrial and Medical Data |
| title_short | Bivariate Power Lindley Models Based on Copula Functions Under Type-II Censored Samples With Applications in Industrial and Medical Data |
| title_sort | bivariate power lindley models based on copula functions under type ii censored samples with applications in industrial and medical data |
| url | http://dx.doi.org/10.1155/jom/5904687 |
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