广义定时截尾下Lomax分布的统计推断及剩余寿命预测  

Statistical inference of Lomax distribution and residual life prediction under generalized Type-Ⅰ censoring

作　　者：龙兵[1] 侯兰宝[1] LONG Bing;HOU Lanbao(School of Mathematics and Physics,Jingchu University of Technology,Jingmen,Hubei 448000,China)

机构地区：[1]荆楚理工学院数理学院,湖北荆门448000

出　　处：《贵州师范大学学报（自然科学版）》2024年第6期59-66,共8页Journal of Guizhou Normal University：Natural Sciences

基　　金：应用数学湖北省重点实验室开放基金资助项目(HBAM202001);教育部协同育人项目(220603584263624);荆楚理工学院科研项目(QN202426)。

摘　　要：在定时截尾试验方案的基础上提出了一种新的截尾试验方案,即广义定时截尾。在广义定时截尾样本下,研究了两参数Lomax分布形状参数和可靠度的极大似然估计。把形状参数的先验分布取为Gamma分布,在三类损失函数下求出了形状参数及可靠度的Bayes估计。分别用经典方法和Bayes方法对元件的剩余使用寿命进行预测,包括点预测和区间预测。对Lomax型元件组成的串联和并联系统的可靠度函数进行估计。通过蒙特卡洛模拟对经典方法和Bayes方法的估计精度进行比较,从均方误差来看,Bayes估计要优于极大似然估计。最后对一个数值例子进行了分析,得出了相关结果。On the basis of Type-Ⅰ censoring scheme,a new censoring test scheme,namely generalized Type-Ⅰ censoring,is proposed.The maximum likelihood estimates of the shape parameter and reliability studied for two-parameter Lomax distribution under generalized Type-Ⅰ censored samples.The prior distribution of the shape parameter is taken as the Gamma distribution,and the Bayesian estimates of the shape parameter and reliability are obtained under three types of loss functions.The remaining useful life of censored components is predicted by using classical method and Bayesian method,including point prediction and interval prediction.The reliability functions of series and parallel systems composed of Lomax components are estimated.Through Monte-Carlo simulation,the estimation accuracy of the classical method and Bayesian method is compared.From the mean squared error point of view,Bayesian estimation is better than maximum likelihood estimation.Finally,a numerical example is analyzed and relevant results are obtained.

关 键 词：Lomax分布 广义定时截尾 先验分布 损失函数 BAYES估计 

分 类 号：O213.2[理学—概率论与数理统计]