三段截尾变量小值概率上界的估计  

Estimates on bounds of probability for three-piece truncated random variables

作　　者：李宗秀[1] 吴捷[2] 

机构地区：[1]黑龙江财经学院基础部,哈尔滨150025 [2]黑龙江科技学院资源与环境工程学院,哈尔滨150027

出　　处：《哈尔滨商业大学学报（自然科学版）》2014年第1期114-116,119,共4页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：国家自然科学基金项目(51103031)

摘　　要：在给定随机变量X∈[-a,M-a],M>0,a≥0,且EX=m1,EX2=m2的条件下,研究了三段线性函数max(0,X,mX-z)的概率分布的上界,其中m>1,z>0,M>max(m1,z/(m-1)).通过简单的变换,将概率问题转化成了均值问题后,应用对偶的理论,构造控制函数,得到了概率分布的上界.是X∈[-a,+∞],a≥0,且EX=m1,EX2=m2,三段线性函数max(0,X,mX-z)的概率分布(左尾)界的推广.具有很强的理论和重要的实际意义.This paper studied the problem of estimating on upper bound of probability and mean for three-piece truncated random variables .Given any random variables X∈[ -a,M-a]with EX =m1,EX2 =m2 for estimations of max （0,X,mX -z）,with m ＆gt;1,z ＆gt;0 , through a simple transformation , probability problems will translate into mean problems .By using dual theory , structural quadratic function , got the probability distribution and mean of the upper.This paper gave any random variables X∈[ -a,＋∞]with EX=m1,EX2 =m2 for probability distribution of the three -piece linear functions max （0,X,mX-z）,which had very important theory and practical significance .

关 键 词：截尾变量 对偶理论 矩问题 控制函数 

分 类 号：O211[理学—概率论与数理统计]