Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values
Majority research studies in the literature determine the weighted coefficients of balanced loss function by suggesting some arbitrary values and then conducting comparison study to choose the best. However, this methodology is not efficient because there is no guarantee ensures that one of the chos...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/5273191 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832560607173279744 |
|---|---|
| author | Fuad S. Al-Duais Mohammed Alhagyan |
| author_facet | Fuad S. Al-Duais Mohammed Alhagyan |
| author_sort | Fuad S. Al-Duais |
| collection | DOAJ |
| description | Majority research studies in the literature determine the weighted coefficients of balanced loss function by suggesting some arbitrary values and then conducting comparison study to choose the best. However, this methodology is not efficient because there is no guarantee ensures that one of the chosen values is the best. This encouraged us to look for mathematical method that gives and guarantees the best values of the weighted coefficients. The proposed methodology in this research is to employ the nonlinear programming in determining the weighted coefficients of balanced loss function instead of the unguaranteed old methods. In this research, we consider two balanced loss functions including balanced square error (BSE) loss function and balanced linear exponential (BLINEX) loss function to estimate the parameter and reliability function of inverse Rayleigh distribution (IRD) based on lower record values. Comparisons are made between Bayesian estimators (SE, BSE, LINEX, and BLINEX) and maximum likelihood estimator via Monte Carlo simulation. The evaluation was done based on absolute bias and mean square errors. The outputs of the simulation showed that the balanced linear exponential (BLINEX) loss function has the best performance. Moreover, the simulation verified that the balanced loss functions are always better than corresponding loss function. |
| format | Article |
| id | doaj-art-8b9e65bdb95d47a3a31bf1a8e719bf0a |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-8b9e65bdb95d47a3a31bf1a8e719bf0a2025-02-03T01:27:08ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/52731915273191Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record ValuesFuad S. Al-Duais0Mohammed Alhagyan1Mathematics Department, College of Humanities and Science in Al Aflaj, Prince Sattam Bin Abdulaziz University, Al Aflaj, Riyadh, Saudi ArabiaMathematics Department, College of Humanities and Science in Al Aflaj, Prince Sattam Bin Abdulaziz University, Al Aflaj, Riyadh, Saudi ArabiaMajority research studies in the literature determine the weighted coefficients of balanced loss function by suggesting some arbitrary values and then conducting comparison study to choose the best. However, this methodology is not efficient because there is no guarantee ensures that one of the chosen values is the best. This encouraged us to look for mathematical method that gives and guarantees the best values of the weighted coefficients. The proposed methodology in this research is to employ the nonlinear programming in determining the weighted coefficients of balanced loss function instead of the unguaranteed old methods. In this research, we consider two balanced loss functions including balanced square error (BSE) loss function and balanced linear exponential (BLINEX) loss function to estimate the parameter and reliability function of inverse Rayleigh distribution (IRD) based on lower record values. Comparisons are made between Bayesian estimators (SE, BSE, LINEX, and BLINEX) and maximum likelihood estimator via Monte Carlo simulation. The evaluation was done based on absolute bias and mean square errors. The outputs of the simulation showed that the balanced linear exponential (BLINEX) loss function has the best performance. Moreover, the simulation verified that the balanced loss functions are always better than corresponding loss function.http://dx.doi.org/10.1155/2021/5273191 |
| spellingShingle | Fuad S. Al-Duais Mohammed Alhagyan Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values Complexity |
| title | Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values |
| title_full | Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values |
| title_fullStr | Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values |
| title_full_unstemmed | Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values |
| title_short | Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values |
| title_sort | nonlinear programming to determine best weighted coefficient of balanced linex loss function based on lower record values |
| url | http://dx.doi.org/10.1155/2021/5273191 |
| work_keys_str_mv | AT fuadsalduais nonlinearprogrammingtodeterminebestweightedcoefficientofbalancedlinexlossfunctionbasedonlowerrecordvalues AT mohammedalhagyan nonlinearprogrammingtodeterminebestweightedcoefficientofbalancedlinexlossfunctionbasedonlowerrecordvalues |