摘要
在Ⅱ型双删失样本下,研究了逆Topp-Leone分布参数的极大似然估计,证明了极大似然估计的存在性和唯一性;基于未知参数的先验分布为Gamma分布和Jeffrey分布,分别在三种不同损失函数下,得到逆Topp-Leone分布未知参数的Bayes估计。根据后验密度函数得到预测密度,进而得到未来观测值在三种损失函数下的预测估计值。为了比较在不同损失下Bayes估计的优劣,采用数值模拟方法计算了各种估计的均值及均方误差,结果表明在Linex损失下未知参数的Bayes估计量更接近真值,均方误差最小。
In the case of type-II doubly censored samples,the maximum likelihood estimation of the inverse Topp-Leone distribution is studied,and the existence and uniqueness of the maximum likelihood estimation are proved.The prior distribution based on the unknown parameters is Gamma distribution and Jeffrey distribution.Under three different loss functions,the Bayes estimation of the unknown parameters of the inverse Topp-Leone distribution is obtained.The predicted density is obtained from the posterior density function,and then the predicted estimated values of the future observations under the three loss functions are obtained.In order to compare the advantages and disadvantages of Bayes estimation under different losses,numerical simulation is used to calculate the mean value and mean square error of various estimators.The results show that the Bayes estimator of unknown parameters under Linex loss is closer to the true value,and the mean squared error is the smallest.
作者
习长新
刘华
张玲
XI Changxin;LIU Hua;ZHANG Ling(School of Mathematics and Physics,Jingchu University of Technology,Jingmen 448000,China;Data Analysis Science Laboratory,Jingchu University of Technology,Jingmen 448000,China)
出处
《荆楚理工学院学报》
2024年第4期1-9,共9页
Journal of Jingchu University of Technology
基金
荆楚理工学院校级科研项目(YB202213)
湖北省自然科学基金项目(2022CFB928)
湖北省教育厅科学研究项目(Q20224302)。