在经典和贝叶斯范式中探讨指数变换逆瑞利分布(ETIRD)

Kahkashan Ateeq, Noumana Safdar, Shakeel Ahmed
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摘要

我们推导了一个新的三参数连续概率分布,称为指数变换逆瑞利分布(ETIRD)。推导了新分布的各种数学性质,包括平均矩、第n矩、矩生成函数、分位数函数等。在经典范式中,使用极大似然方法获得分布的估计量。利用Lindley近似技术,利用非信息先验和信息先验分别在平方误差损失函数(SELF)下得到贝叶斯估计量。通过蒙特卡罗模拟研究,在不同样本量、不同真参数值、有信息先验和无信息先验的情况下,将贝叶斯估计量与相应的极大似然估计量进行了比较。对四个实际数据集进行贝叶斯估计和经典估计的性能判断。仿真研究和实例结果表明,Bayes估计器比mle估计器具有更好的估计效果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Exploring the Exponentiated Transmuted Inverse Rayleigh Distribution (ETIRD) in Classical and Bayesian Paradigms
We derived, a new three parameters continuous probability distribution called Exponentiated Transmuted Inverse Rayleigh Distribution (ETIRD). Various mathematical properties of the new distribution including mean, rth moments, moment generating function, quantile function etc. are derived. In the Classical paradigm, the estimators of the distribution are obtained using the maximum likelihood method. The Bayes estimators are derived under square error loss function (SELF) using non-informative and informative priors via the Lindley approximation technique. Bayes Estimators are compared with their corresponding maximum likelihood Estimators (MLEs) using a Monte Carlo Simulation Study under different sample sizes, different values of true parameters, using informative and non-informative priors. Performance of Bayes estimators and classical estimates is judged for the four real life data sets. The results of simulation study and real-life example show that the Bayes estimators provided better results than MLEs.
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