双定数混合截尾下两参数Pareto分布的统计分析

数学物理学报 ›› 2022, Vol. 42 ›› Issue (1): 269-281.

双定数混合截尾下两参数Pareto分布的统计分析

龙兵^1,*(),张忠占²

¹ 荆楚理工学院数理学院湖北荆门 448000
² 北京工业大学理学部北京 100124

收稿日期:2020-01-11 出版日期:2022-02-26 发布日期:2022-02-23
通讯作者: 龙兵 E-mail:qh-longbing@163.com
基金资助:
国家自然科学基金(11771032);荆楚理工学院科研团队项目(TD202006)

Statistical Analysis of Two-Parameter Pareto Distribution Under Double Type-Ⅱ Hybrid Censoring Scheme

Bing Long^1,*(),Zhongzhan Zhang²

¹ School of Mathematics and Physics, Jingchu University of Technology, Hubei Jingmen 448000
² Faculty of Science, Beijing University of Technology, Beijing 100124

Received:2020-01-11 Online:2022-02-26 Published:2022-02-23
Contact: Bing Long E-mail:qh-longbing@163.com
Supported by:
the NSFC(11771032);the Research Team Project of Jingchu University of Technology(TD202006)

摘要/Abstract

摘要：

在传统的定时和定数截尾试验的基础上，该文首次提出了一种新的截尾试验方案：双定数混合截尾.基于这类截尾数据求出了两参数Pareto分布参数的极大似然估计及θ的置信区间.当α已知时，取Gamma先验分布的情况下，求出了三种不同损失函数下参数θ、可靠度函数以及失效率函数的Bayes估计；当α，θ都未知时，分别取无信息先验分布和指数先验分布，在平方损失函数下分别计算出α，θ、可靠度函数以及失效率函数的Bayes估计.利用Monte-Carlo方法模拟出双定数混合截尾样本，进而得到了两参数Pareto分布的参数及可靠性指标的估计，计算出相对误差并把各种估计的精度进行了比较.最后对一个数值例子进行了分析.

关键词: 两参数Pareto分布, 双定数混合截尾, 极大似然估计, 先验分布, Bayes估计

Abstract:

On the basis of the traditional type-Ⅰ and type-Ⅱ censoring tests, a new type of censoring test scheme, double type-Ⅱ hybrid censoring, is proposed for the first time in this paper. Based on this kind of censored data, the maximum likelihood estimates of the parameters and confidence interval of θ are obtained for two-parameter Pareto distribution. The Bayesian estimates of θ, reliability function and failure rate function under three different loss functions are obtained when α is known and the Gamma prior distribution is selected. When both α and θ are unknown, we take the noninformation prior distribution and exponential prior distribution respectively, and calculate the Bayesian estimates of α and θ, the reliability function and failure rate function under the squared loss function. The Monte-Carlo method is used to simulate double type-Ⅱ hybrid censored samples, the estimates of the parameter and reliability indexes for two-parameter Pareto distribution are obtained. The relative errors are calculated, and the accuracy of various estimates is compared. Finally, a numerical example is analyzed.

Key words: Two-parameter Pareto distribution, Double type-Ⅱ hybrid censoring, Maximum likelihood estimate, Prior distribution, Bayesian estimate

中图分类号:

O213

龙兵,张忠占. 双定数混合截尾下两参数Pareto分布的统计分析[J]. 数学物理学报, 2022, 42(1): 269-281.

Bing Long,Zhongzhan Zhang. Statistical Analysis of Two-Parameter Pareto Distribution Under Double Type-Ⅱ Hybrid Censoring Scheme[J]. Acta mathematica scientia,Series A, 2022, 42(1): 269-281.

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