摘要
逆威布尔分布和广义逐步混合删失方案在可靠性领域中有着广泛的应用,广义逐步混合删失方案能够保证在寿命检测周期内观测到一定数量的失效样本,提高统计推断的效率.因此,文章在该删失方案下从频率学派和贝叶斯学派两个角度讨论了逆威布尔分布的参数推断问题.对于经典频率学方法,文章证明了在此删失方案下两未知参数极大似然估计存在的唯一性,并给出了相应的渐近置信区间,同时,利用EM算法进行点估计,Bootstrap法进行区间估计.对于贝叶斯方法,文章基于伽马先验,利用Metropolis-Hastings算法对两未知参数进行点估计和可信区间估计.最后通过大量的Monte Carlo模拟实验和一组实际数据分析,展示所提出方法的效果.
The inverse Weibull distribution and the generalized progressive hybrid censoring scheme are widely used in the reliability field.The generalized progressive hybrid censoring scheme can ensure that a certain number of failure samples are observed in the life detection cycle,and improve the efficiency of statistical inference.Therefore,we discuss the parameter inference of inverse Weibull distribution from the perspectives of frequency school and Bayesian school under this censored scheme.For the classical frequency method,we prove the existence and uniqueness of the maximum likelihood estimation of two unknown parameters under this censored scheme,and give the corresponding asymptotic confidence interval.At the same time,we use the EM algorithm for point estimation and Bootstrap method for interval estimation.For Bayesian method,we use Metropolis Hastings algorithm to estimate the point and confidence interval of two unknown parameters based on gamma prior.Finally,through a large number of Monte Carlo simulation experiments and a group of actual data analysis,the effect of the proposed method is demonstrated.
作者
张丽平
田茂再
田玉柱
ZHANG Liping;TIAN Maozai;TIAN Yuzhu(School of Statistics and Data Science,Xinjiang University of Finance,Urumqi 830012;School of Statistics,Renmin University of China,Beijing 100872;Northwest Normal University,School of Mathematics and Statistics,Lanzhou 730070)
出处
《系统科学与数学》
CSCD
北大核心
2023年第12期3339-3360,共22页
Journal of Systems Science and Mathematical Sciences
基金
中国人民大学科学研究基金(中央高校基本科研业务费专项资金资助)项目成果(22XNL016)资助课题.
关键词
逆威布尔分布
广义逐步混合删失
参数估计
EM算法
Inverse Weibull distribution
generalized progressive hybrid censoring scheme
parameter estimation
EM algorithm
