On a Logistic Approximation to the Normal and Other Cumulative Distribution Functions

Abstract

This paper proposes an approach that maintains the simplicity of variousapproximations as well as having a closed- form algebraic inverse yet easily generalizable to the approximation of other cumulative distribution functions. The proposed logistic approximation to the normal cumulative distribution function has a maximum error of 0.000560, lower than the maximum error reported by Aludaat et al (2007). Furthermore, the logistic approximation is more flexible in that it can be used to approximate the cumulative distribution functions of other distribution. A Chi-square approximation was also investigated and reported a maximum error of 0.00494.