| 三段截尾变量小值概率上界的估计 |
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| 引用本文： | 李宗秀,吴捷.三段截尾变量小值概率上界的估计[J].黑龙江商学院学报,2014(1):114-116,119. |
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| 作者姓名： | 李宗秀 吴捷 |
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| 作者单位： | [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 |
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| 基金项目： | 国家自然科学基金项目（51103031） |
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| 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。
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| 关 键 词： | 截尾变量 对偶理论 矩问题 控制函数 |
Estimates on bounds of probability for three-piece truncated random variables |
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| LI Zong-xiu,WU Jie.Estimates on bounds of probability for three-piece truncated random variables[J].Journal of Harbin Commercial University(Natural Sciences Edition),2014(1):114-116,119. |
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| Authors: | LI Zong-xiu WU Jie |
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| Institution: | 1. Department of Basic,Heilongjiang University of Finance and Economice, Harbin 150025, China, 2, School of Resources and Environmental Engineering, Heilongjiang Institute of Science and Technology, Harbin 150027, China) |
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| Abstract: | 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 . |
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| Keywords: | truncated variable dual theory moment problem quadratic functions |
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