Philippine E-Journals

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

Roberto N. Padua | Mark S. Borres | Efren O. Barabat

Discipline: Mathematics

 

Abstract:

This paper proposes an approach that maintains the simplicity of various approximations 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.