| 王佳旭,徐宝.加权p、q对称损失函数下Topp-Leone分布的Bayes估计[J].井冈山大学自然版,2025,(5):1-11 |
| 加权p、q对称损失函数下Topp-Leone分布的Bayes估计 |
| BAYES ESTIMATION OF TOPP-LEONE DISTRIBUTION UNDER THE WEIGHTED P AND Q SYMMETRIC LOSS FUNCTION |
| 投稿时间：2025-03-13 修订日期：2025-04-09 |
| DOI：10.3969/j.issn.1674-8085.2025.05.001 |
| 中文关键词: Topp-Leone分布 加权p、q对称损失函数 Bayes估计 可容许性 MCMC算法 |
| 英文关键词: Topp-Leone distribution weighted p and q symmetric loss function Bayes estimation admissibility MCMC algorithm |
| 基金项目:国家自然科学基金项目(11571138); 吉林省科技发展计划项目(YDZJ202201ZYTS622) |
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| 中文摘要: |
| 该文针对加权p、q对称损失函数的场景，运用Bayes参数估计法，对Topp-Leone分布参数的贝叶斯估计形式与性质展开探究。并针对无信息先验分布与共轭先验分布两种情形，成功推导出了参数估计量的精确表达式，从理论上验证了这些估计的可容许性及最小最大估计。经过计算，得到了多层Bayes估计、刀切Bayes估计以及经验Bayes估计。最后，利用R语言软件结合MCMC算法对这些估计进行数值模拟，结果表明，无信息先验分布下的Bayes估计在精度方面优于共轭先验分布下的Bayes估计。 |
| 英文摘要: |
| In the scenario of the weighted p, q symmetric loss function, the Bayes parameter estimation method is used to explore the forms and properties of the Topp-Leone distribution. During this process, the exact forms under the non-informative prior distribution and the conjugate prior distribution are obtained. Meanwhile, the admissibility and minimax estimation of the obtained estimates are proved. Through further calculations, the multi-level Bayes estimates, jackknife Bayes estimates and empirical Bayes are also obtained. Finally, the R language software combined with the MCMC algorithm is utilized to conduct numerical simulations on these estimates. The results show that the Bayes estimates under the non-informative prior distribution are superior to those under the conjugate prior distribution in terms of precision. |
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