由Chvátal定理引出的关于一些无穷可分分布的概率函数的下确界  

THE INFIMUM VALUES OF THE PROBABILITY FUNCTIONS FOR SOME INFINITELY DIVISIBLE DISTRIBUTIONS MOTIVATED BY CHV´ATAL’S THEOREM

作　　者：胡泽春[1] 陆鹏 周倩倩 周兴旺[1] HU Ze-chun;LU Peng;ZHOU Qian-qian;ZHOU Xing-wang(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4期309-316,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,本文研究了概率P(X≤κE[X])的下确界,其中κ是一个正实数, X是一个随机变量.利用分析的方法,我们得到了当随机变量的分布属于无穷可分分布,包括逆高斯分布,对数正态分布, Gumble分布和Logistic分布,时该随机变量不超过其期望的概率的下确界.Motivated by Chv´atal’s theorem,in this paper,we consider the infimum value of the probability P(X≤κE[X]),whereκis a positive real number,and X is a random variable.By employing the analytical method,the results for a random variable whose distribution belongs to some infinitely divisible distributions including the inverse Gaussian,log-normal,Gumbel and logistic distributions are obtained.

关 键 词：Chvátal定理 无穷可分分布 逆高斯分布 对数正态分布 Gumbel分布 Logistic分布 

分 类 号：O211[理学—概率论与数理统计]