Approximations for cumulative distribution function of standard normal

Abstract

In this paper, Tocher’s approximation for standard normal distribution function is improved and three new approximations are proposed. The quality of the new approximations was computed based on two criteria; the maximum absolute error and the mean absolute error. We found that the maximum absolute errors of the proposed approximations fall between 7.62 × 10−7 and 4.95 × 10−5 and the mean absolute errors -based on 5001 values between 0 and 5- fall between 1.82 × 10−7 and 1.59 × 10−5.