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三种抽样设计下Inverse Exponential分布中参数的优良估计

周雅雯, 陈望学, 邓翠红, 杨瑞   

  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.

周雅雯, 陈望学, 邓翠红, 杨瑞. 三种抽样设计下Inverse Exponential分布中参数的优良估计[J]. 系统科学与数学, 2023, 43(4): 1069-1080.

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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[1] Keller A Z, Kamath A, Perera U D. Reliability analysis of CNC machine tools. Reliability Engineering, 1982, 3(6):449-473.
[2] Lin C T, Duran B S, Lewis T O. Inverted gamma as a life distribution. Microelectronics Reliability, 1989, 29(4):619-626.
[3] Singh S K, Singh U, Kumar D. Bayes estimators of the reliability function and parameter of inverted exponential distribution using informative and non-informative priors. Journal of Statistical Computation and Simulation, 2013, 83(12):2258-2269.
[4] Fatima K, Ahmad S P. Bayesian approximation techniques of inverse exponential distribution with applications in engineering. International Journal of Mathematical Sciences and Computing, 2018, 4(2):49-62.
[5] Prakash G. Some estimation procedures for the inverted exponential distribution. South Pacific Journal of Natural and Applied Sciences, 2009, 27(1):71-78.
[6] Dey S. Inverted exponential distribution as a life distribution model from a Bayesian viewpoint. Data Science Journal, 2007, 6(4):107-113.
[7] Prakash G. Inverted exponential distribution under a Bayesian viewpoint. Journal of Modern Applied Statistical Methods, 2012, 11(1):190-202.
[8] Oguntunde P E, Babatunde O S, Ogunmola A O. Theoretical analysis of the Kumaraswamyinverse exponential distribution. International Journal of Statistics and Applications, 2014, 4(2):113-116.
[9] Singh S K, Singh U, Yadav A, et al. On the estimation of stress strength reliability parameter of inverted exponential distribution. International Journal of Scientific World, 2015, 3(1):98-112.
[10] McIntyre G A. A method of unbiased selective sampling, using ranked sets. Austranlian Journal of Agricultural Research, 1952, 3(4):385-390.
[11] Takahasi K, Wakimoto K. On unbiased estimates of the population mean based on the sample stratified by means of ordering. Annals of the Institute of Statistical Mathematics, 1968, 20(1):1-31.
[12] Abu-Dayyeh W, Assrhani A, Ibrahim K. Estimation of the shape and scale parameters of Pareto distribution using ranked set sampling. Statistical Papers, 2013, 54(1):207-225.
[13] Lesitha G, Thomas P Y. Estimation of the scale parameter of a log-logistic distribution. Metrika, 2013, 76(3):427-448.
[14] Wang X L, Lim J, Stokes L. Using ranked set sampling with cluster randomized designs for improved inference on treatment effects. Journal of the American Statistical Association, 2016, 111(516):1576-1590.
[15] Dong X F, Zhang L Y. Estimation of system reliability for exponential distributions based on L ranked set sampling. Communications in Statistics-Theory and Methods, 2020, 49(15):3650-3662.
[16] 杨瑞, 陈望学, 沈炳良,等. 排序集抽样下Power-law分布中参数的参数估计. 系统科学与数学, 2020, 40(2):308-317. (Yang R, Chen W X, Shen B L, et al. Parametric estimator of the Power-Law distribution under ranked set sampling. Journal of Systems Science and Mathematical Sciences, 2020, 40(2):308- 317.)
[17] Qiu G X, Eftekharian A. Extropy information of maximum and minimum ranked set sampling with unequal samples. Communications in Statistics-Theory and Methods, 2021, 50(13):2979-2995.
[18] Qian W S, Chen W X, He X F. Parameter estimation for the Pareto distribution based on ranked set sampling. Statistical Papers, 2021, 62(1):395-417.
[19] Casella G, Berger R L. Statistical Inference. California, USA:Wads Worth and Brooks, 1990.
[20] Mann N R. Optimum estimators for linear functions of location and scale parameters. The Annals of Mathematical Statistics, 1969, 40(6):2149-2155.
[21] Chen W X, Xie M Y, Wu M. Modified maximum likelihood estimator of scale parameter using moving extremes ranked set sampling. Communications in Statistics Simulation and Computation, 2016, 45(6):2232-2240.
[22] Zheng G, Al-Saleh M. Modified maximum likelihood estimators based on ranked set samples. Annals of the Institute of Statistical Mathematics, 2002, 54(3):641-658.
[23] Stokes L. Parametric ranked set sampling. Annals of the Institute of Statistical Mathematics, 1995, 47(3):465-482.
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