由Chvátal定理引出的关于Weibull分布和Pareto分布的研究  

A STUDY ON THE WEIBULL AND PARETO DISTRIBUTIONS MOTIVATED BY CHVATAL'S THEOREM

作　　者：李诚 胡泽春[1] 周倩倩 LI Cheng;HU Ze-chun;ZHOU Qian-qian(College of Mathematics,Sichuan University,Chengdu 610065,China;School of Science,Nanjing University of Posts and Telecommunications,Nanjing 210023,China)

机构地区：[1]四川大学数学学院,四川成都610065 [2]南京邮电大学理学院,江苏南京210023

出　　处：《数学杂志》2024年第3期195-202,共8页Journal of Mathematics

基　　金：Supported by the National Natural Science Foundation of China(12171335,12301603);the Science Development Project of Sichuan University(2020SCUNL201);the Scientific Foundation of Nanjing University of Posts and Telecommunications(NY221026)。

摘　　要：受Chvátal定理的启发,本文研究了随机变量不超过其期望的概率的下确界问题.利用分析的方法,我们得到了当随机变量的分布为Weibull分布或Pareto分布时该随机变量不超过其期望的概率的下确界.Motivated by Chvátal's theorem,in this paper,we consider the infimum value problem on the probability that a random variable is at most its expectation.By employing the analytical method,the results for a random variable with the Weibull distribution or the Pareto distribution are obtained.

关 键 词：Chvátal定理 WEIBULL分布 PARETO分布 

分 类 号：O211[理学—概率论与数理统计]