| 关爽,徐宝.加权平方损失下逆指数分布参数的估计[J].井冈山大学自然版,2024,45(6):1-7 |
| 加权平方损失下逆指数分布参数的估计 |
| ESTIMATION OF THE PARAMETERS OF THE INVERSE EXPONENTIAL DISTRIBUTION UNDER WEIGHTED SQUARE LOSS |
| 投稿时间：2024-05-12 修订日期：2024-06-13 |
| DOI：10.3969/j.issn.1674-8085.2024.06.001 |
| 中文关键词: 逆指数分布 Bayes估计 加权平方损失函数 E-Bayes估计 多层Bayes估计 |
| 英文关键词: inverse exponential distribution Bayes estimation weighted squared loss function E-Bayes estimation multilayer Bayes estimation |
| 基金项目:国家自然科学基金项目(11571138) |
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| 中文摘要: |
| 基于E-Bayes估计和多层Bayes估计的定义，本方法在加权平方损失函数下，首先研究了逆指数分布参数θ的Bayes估计，得出所求的Bayes估计具有可容许性和最小最大性，并进一步讨论参数θ的E-Bayes估计及多层Bayes估计。其次通过研究最大后验区间估计，验证了估计的合理性。最后运用R软件进行数据模拟，并验证了逆指数分布参数估计的仿真性较高。 |
| 英文摘要: |
| Based on the definitions of E-Bayes estimation and multilayer Bayes estimation, this paper firstly investigates the Bayes estimation of inverse exponentially distributed parameters under weighted squared loss function and the admissibility and minimax of the proposed Bayes estimation was discussed. Further, E-Bayes estimation and multi-layer Bayes estimation of the parameters are discussed. Secondly, the reasonableness of the estimation is verified by studying the maximum a posteriori interval estimation. Finally, R software is used to simulate the data and verify that the simulation of inverse exponential distribution parameter estimation is high. |
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