邹路燕, 金良琼, 苏燕青, 陶永, 李琼忆. 双边定数截尾下线性指数分布的参数估计[J]. 内江师范学院学报, 2024, 39(4): 32-38. DOI: 10.13603/j.cnki.51-1621/z.2024.04.006
    引用本文: 邹路燕, 金良琼, 苏燕青, 陶永, 李琼忆. 双边定数截尾下线性指数分布的参数估计[J]. 内江师范学院学报, 2024, 39(4): 32-38. DOI: 10.13603/j.cnki.51-1621/z.2024.04.006
    ZOU Luyan, JIN Liangqiong, SU Yanqing, TAO Yong, LI Qiongyi. Parameter estimation of linear exponential distribution under type-II doubly censored sample[J]. Journal of Neijiang Normal University, 2024, 39(4): 32-38. DOI: 10.13603/j.cnki.51-1621/z.2024.04.006
    Citation: ZOU Luyan, JIN Liangqiong, SU Yanqing, TAO Yong, LI Qiongyi. Parameter estimation of linear exponential distribution under type-II doubly censored sample[J]. Journal of Neijiang Normal University, 2024, 39(4): 32-38. DOI: 10.13603/j.cnki.51-1621/z.2024.04.006

    双边定数截尾下线性指数分布的参数估计

    Parameter estimation of linear exponential distribution under type-II doubly censored sample

    • 摘要: 在双边定数截尾样本下讨论了线性指数分布中未知参数的极大似然估计和Bayes估计.通过Newton-Raphson迭代法得到了参数的极大似然估计,并证明了极大似然估计的唯一存在性.选取无信息先验分布与共轭先验分布,分别在对称损失函数和非对称损失函数下,通过Tierney-Kadane近似讨论参数的Bayes 近似估计.利用MatlabR200b模拟了未知参数的极大似然估计的均方误差以及Bayes估计的均方误差,结果表明:不同样本量不同截尾方案下,选取Gamma先验分布并在平方损失函数下,未知参数的Bayes估计的均方误差是最小的.

       

      Abstract: The maximum likelihood estimation and Bayes estimation of unknown parameters in linear exponential distribution are discussed under the type-II doubly censored sample. The maximum likelihood estimation of unknown parameter is obtained by Newton-Raphson iterative method, and the unique existence of maximum likelihood estimation is proved. The Bayes approximate estimates of the parameters are discussed by Tierney-Kadane approximation under symmetric loss function and asymmetric loss function by selecting non-informative prior distribution and conjugate prior distribution. The mean square error of maximum likelihood estimation and Bayes estimation of unknown parameters is simulated by MatlabR200b. The results show that the mean square error of Bayes estimation of unknown parameters is the smallest when the Gamma prior distribution is selected and the squared loss function is used under different sample sizes and different censored schemes.

       

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