[1]邓严林.双边定数截尾下Topp-Leone分布的Bayes估计与预测[J].江西师范大学学报(自然科学版),2021,(03):272-277.[doi:10.16357/j.cnki.issn1000-5862.2021.03.08]
　DENG Yanlin.The Bayesian Estimation and Prediction for the Topp-Leone Distribution under Type-II Doubly Censored Sample[J].Journal of Jiangxi Normal University:Natural Science Edition,2021,(03):272-277.[doi:10.16357/j.cnki.issn1000-5862.2021.03.08]
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双边定数截尾下Topp-Leone分布的Bayes估计与预测()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2021年03期
页码:
272-277
栏目:
数学与应用数学
出版日期:
2021-06-10

文章信息/Info

Title:
The Bayesian Estimation and Prediction for the Topp-Leone Distribution under Type-II Doubly Censored Sample
文章编号:
1000-5862(2021)03-0272-06
作者:
邓严林
荆楚理工学院数理学院,湖北 荆门 448000
Author(s):
DENG Yanlin
School of Mathematics and Science,Jingchu University of Technology,Jingmen Hubei 448000,China
关键词:
Topp-Leone分布;  双边定数截尾;  Bayes估计;  Bayes预测
Keywords:
Topp-Leone distribution;  Type-II doubly censored sample;  Bayesian estimation;  Bayesian prediction
分类号:
O 213
DOI:
10.16357/j.cnki.issn1000-5862.2021.03.08
文献标志码:
A
摘要:
在双边定数截尾样本下得到了Topp-Leone分布中参数的极大似然估计.基于无信息先验分布和Gamma先验分布,在平方损失和预防损失下分别得到了参数的Bayes估计.根据后验密度函数得到了未知参数的Bayes可信区间和未来观测值的预测密度,进而可得预测值和预测区间.利用Monte-Carlo模拟计算了参数的各种估计的均方误差,研究结果表明:当取Gamma先验分布时,在平方损失下参数的Bayes估计是最优的.最后通过一个寿命数据的例子计算出未知参数的估计以及未来观测值的预测值和预测区间.
Abstract:
In this paper,the maximum likelihood estimation of the parameter in the Topp-Leone distribution is obtained under type-II doubly censored sample.Based on the non-information prior distribution and Gamma prior distribution,the Bayesian estimation of the parameter is obtained under the squared loss and precautionary loss respectively.According to the posterior density function,the Bayesian credible interval of the unknown parameter and the predictive density of future observation are obtained,and then the predictive values and predictive intervals can be obtained.The mean square errors of various estimators are calculated by means of Monte-Carlo simulation,the conclusion is that the Bayesian estimation of the parameter is optimal under the Gamma prior distribution and the squared loss function.Finally,an example of life data is used to calculate the estimation of the unknown parameter,the predictive values and predictive intervals of future observation.

参考文献/References:

[1] Topp C W,Leone F C.A family of J-shaped frequency functions[J].Journal of the American Statistical Association,1955,50(269):209-219.
[2] El-Sayed M A,Abd-Elmougod G A,Abdel-Rahman E O.Estimation for coefficient of variation of Topp-Leone distribution under adaptive Type-II progressive censoring scheme:Bayesian and non-Bayesian approaches[J].Journal of Computational and Theoretical Nanoscience,2015,12(11):4028-4035.
[3] Al-Zahrani B,Alshomrani A A.Inference on stress-strength reliability from Topp-Leone distributions[J].Journal of King Abdulaziz University-Science,2012,24(1):73-88.
[4] Arora S,Mahajan K K,Kumari R.Bayes estimators for the reliability and hazard rate functions of Topp-Leone distribution using Type-II censored data[J].Communications in Statistics:Simulation and Computation,doi:10.1080/03610918.2019.1602646.
[5] MirMostafaee S M T K.On the moments of order statistics coming from the Topp-Leone distribution[J].Statistics and Probability Letters,2014,95(6):85-91.
[6] Feroze N,Aslam M.On Bayesian analysis of failure rate under Topp Leone distribution using complete and censored samples[J].International Journal of Mathematical,Computational,Physical,Electrical and Computer Engineering,2013,7(3):426-432.
[7] MirMostafaee S M T K,Mahdizadeh M,Aminzadeh M,et al.Bayesian inference for the Topp-Leone distribution based on lower k-record values[J].Japan Journal of Industrial and Applied Mathematics,2016,33(3):637-669.
[8] 田霆.双边定数截尾下Weibull分布联合置信区间探讨[J].电子产品可靠性与环境试验,2020,38(1):40-42.
[9] 郭红莹,吴黎军.双边定数截尾下Burr分布参数的Bayes估计[J].黑龙江大学自然科学学报,2015,32(6):735-739.
[10] 李艳玲.双边定数截尾场合双参数指数分布的贝叶斯预测[J].统计与决策,2014(11):68-70.
[11] 杨君慧,师义民,鄢伟安.双边定数截尾试验下广义指数分布的可靠性分析[J].火力与指挥控制,2014,39(3):133-136,147.
[12] 田霆,刘次华,陈家清.双边定数截尾情形下一个两参数有浴盆形状失效率的寿命分布参数的Bayes估计[J].武汉理工大学学报:交通科学与工程版,2012,36(5):1088-1090,1094.
[13] 侯华蕾,师义民,李豪亮.双边定数截尾下Pareto分布的可靠性分析[J].数理统计与管理,2009,28(5):826-830.
[14] 王伟志,袭著有,石月岩,等.双边定数截尾下k(m)/n系统的可靠性分析[J].火力与指挥控制,2013,38(12):130-133.
[15] 周洁,贺兴时,刘俊利.双边定数截尾场合下Burr Ⅻ分布的Bayes估计[J].统计与决策,2014(20):25-27.

备注/Memo

备注/Memo:
收稿日期:2020-11-09
基金项目:教育部人文社科基金(18YJA880056)和荆楚理工学院科研团队课题(TD202006)资助项目.
作者简介:邓严林(1969—),男,湖北钟祥人,副教授,主要从事概率统计研究.E-mail:372165971@qq.com
更新日期/Last Update: 2021-06-10