标准正态分布的简洁闭式

A compact closed form of standard normal distribution

由于不少文献给出的数值闭式相当复杂而不易推广,故采用二维圆近似思想导出了标准正态分布的简洁闭式,从其逆函数角度得到分位点的相应闭式,使概率计算简单易行.另外,还提出主余项积分补偿思想,可获得更为精确的简洁闭式,并给出了误差分布.

It is well known that the probability integral and quantile of a standard normal distribution are usually calculated by table lookup. A lot of literature gave also some approximate formulas, which are very complex and inconvenient to use. In this paper, the compact closed forms of the standard normal distribution and quantile are presented by using the twodimensional circular approximation and inverse function, which make calculation of the probability much easier. Furthermore, we make use of the compensation of primary and remainder integrals to derive more accurately compact closed forms, with the error distributions of the compact closed forms given.