Chernoff bounds are a powerful application of the Markov inequality to produce strong bounds on the tails of probability distributions. They are often used to bound the tail probabilities of sums of Poisson trials, or in regression to produce conservative confidence intervals for the parameters of such trials. The bounds provide expressions for the tail probabilities that can be inverted for a given probability/confidence to provide tail intervals. The inversions involve the solution of transcendental equations and it is often convenient to substitute approximations that can be exactly solved e.g. by the quadratic equation. In this paper we introduce approximations for the Chernoff bounds whose inversion can be exactly solved with a quadratic equation, but which are closer approximations than those adopted previously.

翻译：Chernoff 边框是Markov 不平等的有力应用,目的是在概率分布的尾巴上产生强烈的界限。 它们常常被用来捆绑Poisson试验量的尾部概率, 或者在回归中产生对此类试验参数的保守信任间隔。 边框为尾部概率提供了表达方式, 尾部概率可以被倒置, 给定的概率/ 信心提供尾巴间隔。 反转涉及超度方程的解决方案, 并且通常比较方便地替代近似, 近似可以通过二次方程来完全解决, 例如二次方程。 在本文中, 我们引入 Chernoff 边框的近似值, 后者的反向可完全用二次方程解决, 但近似于先前的近似值 。