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OACSTPCD
THE INFIMUM VALUES OF THE PROBABILITY FUNCTIONS FOR SOME INFINITELY DIVISIBLE DISTRIBUTIONS MOTIVATED BY CHVÁTAL'S THEOREM
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 Chvátal's theorem,in this paper,we consider the infimum value of the probability P(X ≤ κE[X]),where κ is 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.
胡泽春;陆鹏;周倩倩;周兴旺
四川大学数学学院,四川成都 610065南京邮电大学理学院,江苏南京 210023
数学
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
Chvátal's theoreminfinitely divisible distributioninverse gaussian distribu-tionlog-normal distributiongumbel distributionlogistic distribution
《数学杂志》 2024 (004)
309-316 / 8
Supported by the National Natural Science Foundation of China(12171335,12301603),the Science Development Project of Sichuan University(2020SCUNL201)and the Scientific Foundation of Nanjing University of Posts and Telecommunications(NY221026).
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