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### 三种抽样设计下Inverse Exponential分布中参数的优良估计

1. 吉首大学数学与统计学院, 吉首 416000
• 收稿日期:2022-06-28 修回日期:2022-10-11 发布日期:2023-05-18
• 通讯作者: 陈望学, Email:chenwangxue2015@163.com
• 基金资助:
国家自然科学基金(12261036, 11901236),湖南省自然科学面上基 金项目(2022JJ30469),湖南省教育厅重点项目(21A0328), 2020年湖南省教学改革项目(HNJG-2020-0552), 2022年湖南省学位与研究生教学改革研究项目(2022JGZD051), 湖南省青年骨干教师项目(湘教通〔2020〕43 号),2022年湖南省研究生科研创新项目(CX20221113)和2021年吉首大学科研项目(Jdy21013)资助课题.

ZHOU Yawen, CHEN Wangxue, DENG Cuihong, YANG Rui. Optimal Estimation of the Parameter of Inverse Exponential Distribution Under Three Sampling Designs[J]. Journal of Systems Science and Mathematical Sciences, 2023, 43(4): 1069-1080.

### Optimal Estimation of the Parameter of Inverse Exponential Distribution Under Three Sampling Designs

ZHOU Yawen, CHEN Wangxue, DENG Cuihong, YANG Rui

1. Department of Mathematics and Statistics, Jishou University, Jishou 416000
• Received:2022-06-28 Revised:2022-10-11 Published:2023-05-18
Inverse Exponential (IE) 分布作为一种寿命模型, 在生存分析中起着重要作用. 文章分别在简单随机抽样 (SRS), 排序集抽样 (RSS) 和基于 Fisher 信息量最大 RSS (RSSF) 下构造了 IE 分布中参数 $\lambda$ 的一些优良估计. 数值结果表明, 使用同等样本容量的 RSS 样本和 RSSF 样本构造的 RSS 估计和 RSSF 估计比 SRS 估计有效.
Inverse Exponential (IE) distribution is the most exploited distribution for life-time data analysis. In this paper, some optimal estimation of the parameter λ of IE distribution under simple random sampling (SRS), ranked set sampling (RSS) and a RSS version based on the order statistic that maximizes the Fisher information number for a fixed set size (RSSF) will be respectively constructed. Numerical results show that these estimators under RSS and RSSF can be real competitors against the ones based on SRS, when the sample size is used.

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