Approximations for CDF of Standard Normal

Abstract

In this paper, new approximations for the standard normal cumulative distribution function have been proposed. We focused on a set of approximations that take the following form,

0.5(Sqrt(1-exp(-A(z)))

where  A(z) is a polynomial function in z consisting of only two terms. The accuracy of the proposed approximations was compared with the accuracy of some existing approximations in the literature that take the same form. The comparison relied on calculating two well-known measures: the maximum absolute error (MAAE) and the mean absolute error (MEAE). The numerical results showed that the proposed approximations outperformed the approximations that were studied.