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Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values

作     者:Al-Duais, Fuad S. Alhagyan, Mohammed 

作者机构:Prince Sattam Bin Abdulaziz Univ Coll Humanities & Sci Al Aflaj Math Dept Riyadh Saudi Arabia Thamar Univ Adm Sci Coll Adm Dept Thamar Yemen 

出 版 物:《COMPLEXITY》 (Complexity)

年 卷 期:2021年第2021卷第1期

核心收录:

学科分类:07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主  题:Nonlinear programming 

摘      要: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.

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