摘要
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 lookup. 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 twodimensional 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.
出处
《西安电子科技大学学报》
EI
CAS
CSCD
北大核心
2003年第3期289-292,共4页
Journal of Xidian University
基金
国家自然科学基金资助项目(69931030)
关键词
标准正态分布
分位点
二维圆近似
简洁闭式
主余项积分补偿
误差分布
standard normal distribution
quantile
two-dimensional approximation
compact closed form
primary and remainder integrals compensation
