不同形式损失函数下广义瑞利分布的贝叶斯和e -贝叶斯估计及其实际应用

IF 0.7 Q2 MATHEMATICS
E. M. Eldemery, A. M. Abd-Elfattah, K. M. Mahfouz, Mohammed M. El Genidy
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引用次数: 0

摘要

本文研究了基于ii型截尾数据的广义瑞利分布的未知形状参数的贝叶斯估计和期望贝叶斯估计。随后,使用四种不同的损失函数:线性指数损失函数、加权线性指数损失函数、复合线性指数损失函数和加权复合线性指数损失函数获得这些估计量。加权复合线性指数损失函数是将权重与复合线性指数损失函数相结合而产生的一种新型建议损失函数。我们使用分布作为先验分布。此外,通过超参数的三种不同的先验分布得到了期望贝叶斯估计量。此外,根据四种不同形式的损失函数,使用蒙特卡罗模拟执行贝叶斯和期望贝叶斯估计技术,以验证所建议的损失函数的有效性,并比较贝叶斯和期望贝叶斯估计方法。此外,仿真结果表明,在均方误差最小的情况下,本文提出的加权复合线性指数损失函数对应的贝叶斯估计和期望贝叶斯估计的性能明显优于其他损失函数,期望贝叶斯估计也优于贝叶斯估计。最后,使用一组来自医学领域的真实数据来证明所提出的技术,以阐明所建议的估计器对真实现象的适用性,并表明所讨论的加权复合线性指数损失函数是有效的,可以应用于现实场景。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Bayesian and E-Bayesian Estimation for the Generalized Rayleigh Distribution under Different Forms of Loss Functions with Real Data Application
This paper investigates the estimation of an unknown shape parameter of the generalized Rayleigh distribution using Bayesian and expected Bayesian estimation techniques based on type-II censoring data. Subsequently, these estimators are obtained using four different loss functions: the linear exponential loss function, the weighted linear exponential loss function, the compound linear exponential loss function, and the weighted compound linear exponential loss function. The weighted compound linear exponential loss function is a novel suggested loss function generated by combining weights with the compound linear exponential loss function. We use the gamma distribution as a prior distribution. In addition, the expected Bayesian estimator is obtained through three different prior distributions of the hyperparameters. Moreover, depending on the four distinct forms of loss functions, Bayesian and expected Bayesian estimation techniques are performed using Monte Carlo simulations to verify the effectiveness of the suggested loss function and to compare Bayesian and expected Bayesian estimation methods. Furthermore, the simulation results indicate that, depending on the minimum mean squared error, the Bayesian and expected Bayesian estimations corresponding to the weighted compound linear exponential loss function suggested in this paper have significantly better performance compared to other loss functions, and the expected Bayesian estimator also performs better than the Bayesian estimator. Finally, the proposed techniques are demonstrated using a set of real data from the medical field to clarify the applicability of the suggested estimators to real phenomena and to show that the discussed weighted compound linear exponential loss function is efficient and can be applied in a real-life scenario.
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