In this paper we first use the distribution of the number of records to demonstrate that the right tail probabilities of counts of rare events are generally better approximated by the right tail probabilities of a Poisson distribution than those of the normal distribution. We then show that the moderate deviations in Poisson approximation generally require an adjustment and, with suitable adjustment, we establish better error estimates of the moderate deviations in Poisson approximation than those in [18]. Our estimates contain no unspecified constants and are easy to apply. We illustrate the use of the theorems via six applications: Poisson-binomial distribution, the matching problem, the occupancy problem, the birthday problem, random graphs, and 2-runs. The paper complements the works [16], [8], and [18].

中文翻译：

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关于泊松近似的中度偏差

在本文中，我们首先使用记录数的分布来证明，与正态分布相比，泊松分布的右尾概率通常更好地近似于罕见事件计数的右尾概率。然后，我们表明泊松近似中的中度偏差通常需要调整，并且通过适当的调整，我们对泊松近似中的中度偏差建立了比 [18] 中更好的误差估计。我们的估计不包含未指定的常数并且易于应用。我们通过六个应用来说明这些定理的使用：泊松二项分布、匹配问题、占用问题、生日问题、随机图和 2 次运行。本文补充了作品 [16]、[8] 和 [18]。