基于下记录值逆Rayleigh模型的估计及预测  

Estimation and prediction of the inverse Rayleigh model based on lower record values

作　　者：席吉富 苏彦玉 肖静怡 罗子怡 程丹 龙兵[1] XI Jifu;SU Yanyu;XIAO Jingyi;LUO Ziyi;CHENG Dan;LONG Bing(School of Mathematics and Physics,Jingchu University of Technology,Jingmen 448000,China)

机构地区：[1]荆楚理工学院数理学院,湖北荆门448000

出　　处：《高师理科学刊》2024年第1期12-17,共6页Journal of Science of Teachers＇College and University

基　　金：荆楚理工学院教育教学研究项目(JX2022-011);2023年湖北省大学生创新创业训练计划项目(S202311336055)。

摘　　要：当观测数据是下记录值时,利用经典方法讨论了逆Rayleigh分布未知参数的极大似然估计和一致最小方差无偏估计,进而得到了可靠度及失效率的极大似然估计.取未知参数的先验分布为Gamma分布,在平方损失函数下讨论了逆Rayleigh模型的未知参数、概率密度函数、累积分布函数及系统可靠度的Bayes估计,并对元件的剩余寿命进行预测.通过蒙特卡洛模拟研究了估计量的性质,借助数值实验对估计量的值进行计算.When the observed data are the lower record values,the maximum likelihood estimation and uniform minimum variance unbiased estimation of the unknown parameter for the inverse Rayleigh distribution are discussed by using the classical method,and the maximum likelihood estimates of the reliability and failure rate are obtained.Taking Gamma distribution as prior distribution of the unknown parameter,the Bayesian estimates of the unknown parameter,probability density function,cumulative distribution function and system reliability of the inverse Rayleigh model are discussed under the squared loss function,and the remaining lifetime of the component is predicted.The properties of the estimators are studied through Monte-Carlo simulation.Finally,numerical examples are used to calculate the values of the estimators.

关 键 词：逆Rayleigh分布 下记录值 先验分布 BAYES估计 预测区间 

分 类 号：O213.2[理学—概率论与数理统计]