A logistic approximation to the cumulative normal distribution
Abstract: This paper develops
a logistic approximation to the cumulative normal distribution. Although the
literature contains a vast collection of approximate functions for the normal
distribution, they are very complicated, not very accurate, or valid for only a
limited range. This paper proposes an enhanced approximate function. When
comparing the proposed function to other approximations studied in the
literature, it can be observed that the proposed logistic approximation has a
simpler functional form and that it gives higher accuracy, with the maximum
error of less than 0.00014 for the entire range. This is, to the best of the
authors’ knowledge, the lowest level of error reported in the literature. The
proposed logistic approximate function may be appealing to researchers,
practitioners and educators given its functional simplicity and mathematical
accuracy.
Author: Shannon R. Bowling,
Mohammad T. Khasawneh, Sittichai Kaewkuekool, Byung Rae Cho
Journal Code: jptindustrigg090017
