论文标题
关于由Chvátal的猜想促进的泊松，几何和帕斯卡分布的研究
A study on the Poisson, geometric and Pascal distributions motivated by Chvátal's conjecture
论文作者
论文摘要
令$ b（n，p）$表示参数$ n $和$ p $的二项式随机变量。 vasěkChvátal猜想，对于任何固定的$ n \ geq 2 $，$ m $范围超过$ \ {0，\ ldots，n \} $，概率$ q_m：= p（b（n，m/n）\ leq m）$是$ m $是$ m $是最小的，当$ m $是$ \ $ \ frac $ \ frac} $时。该猜想最近已解决。在本文中，我们考虑到相应的最小值问题的动机是在随机变量不超过其期望的概率上，当它的分布是泊松分布，几何分布或pascal分布时。
Let $B(n,p)$ denote a binomial random variable with parameters $n$ and $p$. Vasěk Chvátal conjectured that for any fixed $n\geq 2$, as $m$ ranges over $\{0,\ldots,n\}$, the probability $q_m:=P(B(n,m/n)\leq m)$ is the smallest when $m$ is closest to $\frac{2n}{3}$. This conjecture has been solved recently. Motivated by this conjecture, in this paper, we consider the corresponding minimum value problem on the probability that a random variable is not more than its expectation, when its distribution is the Poisson distribution, the geometric distribution or the Pascal distribution.
