Improvement Bryc’s Approximation to the Cumulative Distribution Function

Abderrahmane Malki

Abstract

We develop two news approximations to the cumulative distribution function. We begin by improving the accuracy of Cadwell’s approximation. We reduce the accuracy from 0.006466 to 1.6635e-004. For the second approximation we reduce the accuracy of Bryc’s approximation from 7.062e-004 to 2.072e-005. As a performance, we use a Maximum Absolute Error (M.A.E.). We recommend these two new approximations for their high accuracy.