两个广泛相依随机变量在最值运算下的次指数性  

The Subexponentiality for Two Widely Dependent Random Variables Under the Operations of Minimum and Maximum

作　　者：刘庆庆[1] 陈岑[1] 汪世界[1] 

机构地区：[1]安徽大学数学科学学院,合肥230601

出　　处：《应用数学学报》2017年第2期279-286,共8页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11226207);安徽省杰出青年基金(1508085J06);安徽省高等学校自然科学研究基金(KJ2014A020)资助项目

摘　　要：本文主要研究一类广泛相依结构下两个次指数随机变量的最小值、最大值关于次指数族的封闭性.证明了在该相依结构下两个次指数随机变量的最小值总是次指数的,给出了该相依结构下两个次指数随机变量的最大值为次指数分布的一个充分必要条件,推广了已有结果,同时表明该相依结构对两个次指数分布在最值运算下的次指数性是不敏感的.This paper mainly investigates the closure properties about the subexponential class for the minimum and maximum of two subexponential random variables according to a wide type of dependence structure. It is proven that the minimum of two subexponential random variables under such a dependence structure is still subexponential. It also gives a sufficient and necessary condition which ensures that the maximum of two subexponential random variables under this dependence structure is subexponential. The obtained results generalize some existing ones in the literature, which imply that the dependence structure is insensitive to the subexponentiality for two subexponential random variables under the operations of minimum and maximum.

关 键 词：相依结构 次指数分布 长尾分布 最小值 最大值 

分 类 号：O211.4[理学—概率论与数理统计]