广义逐步混合删失方案下Pareto分布的参数推断  

Parameter inference of Pareto distribution under generalized progressive hybrid censoring scheme

作　　者：郝雪青 田茂再[1,2] HAO Xueqing;TIAN Maozai(School of Statistics and Data Science,Xinjiang University of Finance and Economics,Urumqi 830012,China;School of Statistics,Renmin University of China,Beijing 100872,China)

机构地区：[1]新疆财经大学统计与数据科学学院,乌鲁木齐830012 [2]中国人民大学统计学院,北京100872

出　　处：《哈尔滨商业大学学报(自然科学版)》2025年第2期214-218,共5页Journal of Harbin University of Commerce:Natural Sciences Edition

摘　　要：Pareto分布和广义逐步混合删失方案已被广泛应用于经济学、工程学和可靠性等领域,广义逐步混合删失方案不仅允许在产品失效发生前进行随机删除未失效产品来节省时间和成本,而且还保证了在测试中出现一定数量的失效观测.为了提高统计推断的效率,基于极大似然法及贝叶斯方法研究了广义逐步混合删失数据下Pareto分布的形状参数估计.对于经典频率学方法,推导出其对数似然并证明了在此删失方案下该参数的极大似然估计存在且唯一性.对于贝叶斯方法,基于伽马先验,对该参数进行点估计.通过大量的随机模拟对参数估计式进行了模拟检验,模拟结果表明贝叶斯法的估计精度较高,且优于极大似然估计的效果.Pareto distributions and generalized progressive hybrid censoring scheme had been widely used in the fields of economics,engineering,and reliability,et al.Generalized progressive hybrid censoring schemes not only allowed for random deletion of unfailed products before failure occurred to save time and cost,but also ensured that a certain number of failure observations appeared in the test.Therefore,in order to improve the efficiency of statistical inference,investigated the shape parameter estimation of the Pareto distribution under generalized progressive hybrid censoring data based on the maximum likelihood estimation and Bayesian estimation.For the classical frequency method,its log-likelihood was derived and the existence and uniqueness of the maximum likelihood estimation of this parameter under this censoring scheme were proved.For the Bayesian method,a point estimate of this parameter was made based on a gamma prior.The parameter estimator was tested through a large number of stochastic simulations,and the simulation results showed that the estimation accuracy of the Bayesian method was high and its estimation was better than that of the maximum likelihood estimation.

关 键 词：PARETO分布 广义逐步混合删失 参数估计 极大似然估计 贝叶斯估计 

分 类 号：O212[理学—概率论与数理统计]