论文标题
累积标准正态分布和相关功能的Polya上限的改进
Improvements of Polya Upper Bound for Cumulative Standard Normal Distribution and Related Functions
论文作者
论文摘要
尽管关于累积标准正态分布的上限有广泛的文献，但对于感兴趣的参数x的所有值都没有相对清晰。本文的目的是为标准正态分布函数建立一个尖锐的上限，因为其与PHI（X）的最大绝对差异小于x的所有值。已建立的界限改善了众所周知的Polya上限，并且可以用作非常令人满意的精度作为PHI（X）本身的近似值。已经实现了所提出的上限与其他一些现有上限之间的数值比较，这表明所提出的界限比文献中发现的替代边界更紧密。
Although there is an extensive literature on the upper bound for cumulative standard normal distribution, there are relatively not sharp for all values of the interested argument x. The aim of this paper is to establish a sharp upper bound for standard normal distribution function, in the sense that its maximum absolute difference from phi(x) is less than for all values of x. The established bound improves the well-known Polya upper bound and it can be used as an approximation for Phi(x) itself with a very satisfactory accuracy. Numerical comparisons between the proposed upper bound and some other existing upper bounds have been achieved, which show that the proposed bound is tighter than alternative bounds found in the literature.
