A compact closed form of standard normal distribution
Liang Chang · Journal of Xidian University · 2003
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.