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| 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. |
| 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 |
| DOI： |
| 分类号:O211 |
| 基金项目: |
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| THE INFIMUM VALUES OF THE PROBABILITY FUNCTIONS FOR SOME INFINITELY DIVISIBLE DISTRIBUTIONS MOTIVATED BY CHVáTAL'S THEOREM |
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HU Ze-chun,LU Peng,ZHOU Qian-qian,ZHOU Xing-wang
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| Abstract: |
| 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. |
| Key words: Chvátal's theorem infinitely divisible distribution inverse gaussian distribution log-normal distribution gumbel distribution logistic distribution |
