阿基米德Copula下一般随机序的性质  

Some properties of usual stochastic order under Archimedean Copula

作　　者：关清元 王炳兴[1] 钱昊 赵添鑫 GUAN Qing-yuan;WANG Bing-xing;QIAN Hao;ZHAO Tian-xin(School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018,China;College of Mathematics and Computer Science,Wuyi University,Wuyishan 354300,China;Fujian Key Laboratory of Big Data Application and Intellectualization for Tea Industry,Wuyishan 354300,China;The Key Laboratory of Cognitive Computing and Intelligent Information Processing of Fujian Education Institutions,Wuyishan 354300,China)

机构地区：[1]浙江工商大学统计与数学学院,浙江杭州310018 [2]武夷学院数学与计算机学院,福建武夷山354300 [3]福建省茶产业大数据应用与智能化重点实验室,福建武夷山354300 [4]福建省认知计算与智能信息处理高校重点实验室,福建武夷山354300

出　　处：《高校应用数学学报（A辑）》2023年第2期137-150,共14页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11871431);浙江省重点建设高校优势特色学科(浙江工商大学统计学)(1020JYN4120004G-093)。

摘　　要：文中研究了相依随机变量的一般随机序性质.将独立随机变量一般随机序的两个特征推广到了阿基米德Copula下的相依随机变量.此外还给出了阿基米德Copula相依随机变量的两个闭合性质.研究了两个相依随机变量集的最小和最大次序统计量满足一般随机序的充分条件.用几个数值例子验证所得结果.探讨了这些结果在系统可靠性和精算学中的一些潜在应用.In this paper,the ordering properties of usual stochastic order of the dependent random variables are studied.Two characterizations of the usual stochastic order under independent random variables are extended to the dependent random variables under Archimedean Copula.In addition,two closure properties of the random variables with Archimedean Copula are given.The suffcient conditions on the minimum and maximum order statistics of two interdependent random variable sets under the usual stochastic order are provided.Several numerical examples are used to verify our results.Some potential applications of our results in system reliability and actuarial science are discussed.

关 键 词：阿基米德COPULA 一般随机序 优化序 异质组合 

分 类 号：O211.6[理学—概率论与数理统计]