New approximations for standard normal distribution function

Abstract

This article proposes nine new approximations for the standard normal cumulative distribution function In addition, it collects most of the approximations existing in the literature. The accuracy of the proposed approximations is evaluated by using the maximum absolute error and the mean absolute error. The maximum absolute errors fall between 0.0422613 × 10−6 and 950.55 × 10−6, which indicates high accuracy for some of them. A comparison study between the different existing approximations and the proposed approximations is also accomplished.