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中国科学院大学学报 ›› 2011, Vol. 28 ›› Issue (2): 147-154.DOI: 10.7523/j.issn.2095-6134.2011.2.003

• 论文 • 上一篇    下一篇

指数分布定数截尾数据下刻度参数的经验Bayes估计

李翔, 韦来生   

  1. 中国科学技术大学统计与金融系, 合肥 230026
  • 收稿日期:2009-12-11 修回日期:2010-06-17 发布日期:2011-03-15
  • 基金资助:

    国家自然科学基金 (10771204) 和中国科学院知识创新工程重要方向项目 (KJCX3-SYW-S02) 资助 

Empirical Bayes estimation for scale parameter on type-Ⅱ censored samples in exponential distribution

LI Xiang, WEI Lai-Sheng   

  1. University of Science & Technology of China, Hefei 230026, China
  • Received:2009-12-11 Revised:2010-06-17 Published:2011-03-15

摘要:

在指数分布定数截尾情形下,当先验分布中的超参数部分未知时,在加权平方损失下构造了刻度参数的参数型经验Bayes(PEB)估计,研究了其在均方误差 (MSE) 准则下相对于一致最小方差无偏估计 (UMVUE) 的优良性,并获得了 PEB 估计的大样本性质.当先验分布中的超参数完全未知时,通过数值模拟比较了 PEB 估计和 UMVUE 的均方误差,获得了其优良性.最后,通过数值模拟的结果,获得了PEB区间估计的优良性.

关键词: 刻度参数, 指数分布, PEB 估计, MSE准则, 收敛速度

Abstract:

We consider type-Ⅱ censored samples of the exponential distribution. In the case that the hyper-parameters of prior distribution are partly unknown, we construct the parametic empirical Bayes (PEB) estimation for scale parameter with the weighted square-error loss function, study the superiority of PEB estimation over the uniformly minimum variance unbiased estimation (UMVUE) in terms of the mean-square error (MSE) criterion, and obtain its large sample properties. In the case that the hyper-parameters of prior distribution are all unknown, we get the superiority of PEB estimation over UMVUE by comparing the simulated MSE. Finally, we show the superiority of PEB interval estimation by simulation results.

Key words: scale parameter, exponential distribution, PEB estimation, MSE criterion, convergence rate

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