基于双定时混合截尾数据Gompertz分布的统计分析  

Statistical analysis of Gompertz distribution based on double type-Ⅰhybrid censored data

作　　者：龙沁怡 徐丽平[1] LONG Qin-yi;XU Li-ping(School of Information and Mathematics,Yangtze University,Jingzhou 434023,China)

机构地区：[1]长江大学信息与数学学院,湖北荆州434023

出　　处：《东北师大学报（自然科学版）》2023年第3期49-55,共7页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11901058).

摘　　要：假设受试样品的寿命服从Gompertz分布,基于双定时混合截尾数据在2种损失函数下求出了形状参数的Bayes估计.取超参数的3个先验分布计算出形状参数的E-Bayes估计.利用经典方法得到了未来次序失效时刻的点预测和区间预测.当形状参数的共轭先验分布取为Gamma分布时,利用Bayes方法得到了未来次序失效时刻的预测值和等尾预测区间.通过随机模拟计算出形状参数的均值及绝对值相对偏差.通过一个数值例子对文中的结论进行了计算.Assuming that the lifetimes of the tested samples follow Gompertz distribution,the Bayesian estimates of the shape parameter are obtained under two loss functions based on the double type-Ⅰhybrid censored data.The E-Bayes estimates of the shape parameter are calculated by taking three prior distributions of the hyper-parameters.The point prediction and interval prediction of future failure times are obtained by using the classical approach.When the conjugate prior distribution of the shape parameter is taken as Gamma distribution,the Bayesian approach is used to obtain the predictive values and equal-tailed prediction intervals of future failure times.The mean value and relative deviation of the shape parameter are calculated by random simulation.A numerical example is used to calculate the conclusions.

关 键 词：Gompertz分布 双定时混合截尾 E-BAYES估计 BAYES预测 

分 类 号：O213.2[理学—概率论与数理统计]