论文标题
二项式和泊松概率的一些不平等现象
Some inequalities on Binomial and Poisson probabilities
论文作者
论文摘要
令$ s $和$ x $是独立的随机变量，假设在非阴性整数中的值，并进一步假设两个$ \ m athbb {e}（s）$和$ \ m mathbb {e}（x）$都是整数满足$ \ mathbb {e}（e}（s）\ ge ge \ ge \ mathbb bb bb bb {e}（x）我们为尾巴概率$ \ mathbb {p}（s \ ge \ mathbb {e}（s））$建立了足够的条件，以大于$ \ mathbb {p}（s+x \ ge \ ge \ ge \ mathbb {e}（s+x））$。我们还将此结果应用于独立的二项式和泊松随机变量的总和。
Let $S$ and $X$ be independent random variables, assuming values in the set of non-negative integers, and suppose further that both $\mathbb{E}(S)$ and $\mathbb{E}(X)$ are integers satisfying $\mathbb{E}(S)\ge \mathbb{E}(X)$. We establish a sufficient condition for the tail probability $\mathbb{P}(S\ge \mathbb{E}(S))$ to be larger than $\mathbb{P}(S+X\ge \mathbb{E}(S+X))$. We also apply this result to sums of independent binomial and Poisson random variables.
