Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values
The essential objective of this research is to develop a linear exponential (LINEX) loss function to estimate the parameters and reliability function of the Weibull distribution (WD) based on upper record values when both shape and scale parameters are unknown. We perform this by merging a weight in...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/9982916 |
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| author | Fuad S. Al-Duais |
| author_facet | Fuad S. Al-Duais |
| author_sort | Fuad S. Al-Duais |
| collection | DOAJ |
| description | The essential objective of this research is to develop a linear exponential (LINEX) loss function to estimate the parameters and reliability function of the Weibull distribution (WD) based on upper record values when both shape and scale parameters are unknown. We perform this by merging a weight into LINEX to produce a new loss function called the weighted linear exponential (WLINEX) loss function. Then, we utilized WLINEX to derive the parameters and reliability function of the WD. Next, we compared the performance of the proposed method (WLINEX) in this work with Bayesian estimation using the LINEX loss function, Bayesian estimation using the squared-error (SEL) loss function, and maximum likelihood estimation (MLE). The evaluation depended on the difference between the estimated parameters and the parameters of completed data. The results revealed that the proposed method is the best for estimating parameters and has good performance for estimating reliability. |
| format | Article |
| id | doaj-art-5dc3e05fe8334afa8a13832f0685e9d5 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-5dc3e05fe8334afa8a13832f0685e9d52025-02-03T01:04:08ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/99829169982916Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record ValuesFuad S. Al-Duais0Mathematics Department, College of Humanities and Science in Al Aflaj, Prince Sattam Bin Abdulaziz University, Al Aflaj, Saudi ArabiaThe essential objective of this research is to develop a linear exponential (LINEX) loss function to estimate the parameters and reliability function of the Weibull distribution (WD) based on upper record values when both shape and scale parameters are unknown. We perform this by merging a weight into LINEX to produce a new loss function called the weighted linear exponential (WLINEX) loss function. Then, we utilized WLINEX to derive the parameters and reliability function of the WD. Next, we compared the performance of the proposed method (WLINEX) in this work with Bayesian estimation using the LINEX loss function, Bayesian estimation using the squared-error (SEL) loss function, and maximum likelihood estimation (MLE). The evaluation depended on the difference between the estimated parameters and the parameters of completed data. The results revealed that the proposed method is the best for estimating parameters and has good performance for estimating reliability.http://dx.doi.org/10.1155/2021/9982916 |
| spellingShingle | Fuad S. Al-Duais Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values Complexity |
| title | Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values |
| title_full | Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values |
| title_fullStr | Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values |
| title_full_unstemmed | Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values |
| title_short | Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values |
| title_sort | bayesian estimations under the weighted linex loss function based on upper record values |
| url | http://dx.doi.org/10.1155/2021/9982916 |
| work_keys_str_mv | AT fuadsalduais bayesianestimationsundertheweightedlinexlossfunctionbasedonupperrecordvalues |