针对定时截尾指数寿命数据的参数估计问题,采用排序集抽样方法,研究了指数分布参数的极大似然估计.针对排序集抽样下似然方程求不出解的问题,似然方程的部分项替换为期望,并给出修正极大似然估计.估计效率的比较结果说明:基于排序集抽样方法的修正估计量优于基于简单随机抽样方法的极大似然估计量.
In order to solve the problem of parameter estimation for time censored exponential life data, the maximum likelihood estimation using ranked set sampling method is studied. For the problem that likelihood equation’s root under ranked set sampling is not found, some terms of likelihood equation are replaced with their expectations, and the modified maximum likelihood estimation is given. The comparison results of estimation efficiencies show that the proposed estimator using ranked set sampling method is better than maximum likelihood estimator using simple random sampling method.
[1] CHEN Z H, BAI Z D, SINHA B K. Ranked set sampling-theory and application[M]. New York: Springer, 2004.
[2] WANG X L, LIM J, STOKES L. Using ranked set sampling with cluster randomized designs for improved inference on treatment effects[J]. J Am Stat Assoc, 2016, 111(516): 1576-1590. DOI:10.1080/01621459.2015.1093946.
[3] FREY J, ZHANG Y M. An algorithm with applications in ranked-set sampling[J]. J Stat Comput Simul, 2018, 88(3): 471-481. DOI:10.1080/00949655.2017.1392526.
[4] AWAIS M, HAQ A. A new cumulative sum control chart for monitoring the process mean using varied L ranked set sampling[J]. Journal of Industrial and Production Engineering, 2018, 35(2): 74-90. DOI: 10.1080/21681015.2017.1417787.
[5] ATA TUTKUN N, KOYUNCU N, KARABEY U. Discrete-time survival analysis under ranked set sampling: an application to Turkish motor insurance data[J]. J Stat Comput Simul, 2019, 89(4): 660-667. DOI:10.1080/00949655.2018.1564308.
[6] 董晓芳,张良勇,王志军.基于非均等排序集抽样的Wilcoxon符号秩检验[J].河北大学学报(自然科学版), 2020, 40(3): 225-231. DOI:10.3969/j.issn.1000-1565.2020.03.001.
[7] 曹晋华,程侃.可靠性数学引论[M].2版.北京: 高等教育出版社, 2006.
[8] BHOJ D S. New ranked set sampling for one-parameter family of distributions[J]. Biometrical Journal, 2000, 42(5):647-658. DOI: 10.1002/1521-4036(200009)42:5<647::AID-BIMJ647>3.0.CO;2-B.
[9] ZHENG G, AL-SALEH M F. Modified maximum likelihood estimators based on ranked set samples[J]. Ann Inst Stat Math, 2002, 54(3): 641-658. DOI:10.1023/A: 1022475413950.
[10] SHADID M R, RAQAB M Z, AL-OMARI A I. Modified BLUEs and BLIEs of the location and scale parameters and the population mean using ranked set sampling[J]. J Stat Comput Simul, 2011, 81(3): 261-274. DOI:10.1080/00949650903277271.
[11] CHACKO M. Bayesian estimation based on ranked set sample from Morgenstern type bivariate exponential distribution when ranking is imperfect[J]. Metrika, 2017, 80(3): 333-349. DOI: 10.1007/s00184-016-0607-7.
[12] CHEN W X, TIAN Y, XIE M Y. Maximum likelihood estimator of the parameter for a continuous one-parameter exponential family under the optimal ranked set sampling[J]. J Syst Sci Complex, 2017, 30(6): 1350-1363. DOI:10.1007/s11424-017-6135-3.
[13] 董晓芳,张良勇.排序集抽样下指数分布的产品可靠度研究[J].运筹与管理,2020, 29(7): 99-104. DOI: 10.12005/orms.2020.0177.
[14] 张良勇,董晓芳.排序集抽样下随机截尾数据的平均寿命估计[J].河北大学学报(自然科学版),2022,42(2):113-117.DOI:103969/j.issn.1000-1565.2022.02.001.
[15] MEHROTRA K G, NANDA P. Unbiased estimator of parameter by order statistics in the case of censored samples[J]. Biometrika, 1974, 61(3): 601-606. DOI: 10.2307/2334745.
[16] 董晓芳,张良勇.基于排序集抽样方法的可靠性估计[M].北京:科学出版社, 2021. (
