Improved Inequalities for the Poisson and Binomial Distribution and Upper Tail Quantile Functions
Improved Inequalities for the Poisson and Binomial Distribution and Upper Tail Quantile Functions
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泊松和二项分布以及上尾分位数函数的改进不等式
DOI：
10.1155/2013/412958
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
M. Short
中科院分区：
文献类型：
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作者：
M. Short
泊松和二项累积分布和逆（分位数）函数的精确计算对于某些应用可能太具有挑战性或不必要，并且在某些情况下可能需要更简单的解决方案（通常通过应用正态近似或指数不等式获得）。尽管正态分布近似很容易应用并且可能非常准确，但错误符号通常是未知的;错误符号通常因指数不等式而闻名，但代价是一些悲观主义。在本文中，最近的工作描述有关的正态分布函数和二项式分布函数的普遍不等式扩展到包括泊松分布函数，新的分位数函数不等式，然后获得这两种分布。指数界-这改善后的Bauff-Hoeffding不等式的一个因素，至少有两个-也得到了这两种分布。
The exact evaluation of the Poisson and Binomial cumulative distribution and inverse (quantile) functions may be too challenging or unnecessary for some applications, and simpler solutions (typically obtained by applying Normal approximations or exponential inequalities) may be desired in some situations. Although Normal distribution approximations are easy to apply and potentially very accurate, error signs are typically unknown; error signs are typically known for exponential inequalities at the expense of some pessimism. In this paper, recent work describing universal inequalities relating the Normal and Binomial distribution functions is extended to cover the Poisson distribution function; new quantile function inequalities are then obtained for both distributions. Exponential bounds—which improve upon the Chernoff-Hoeffding inequalities by a factor of at least two—are also obtained for both distributions.