A Sharp Polya-Based Approximation to the Normal CDF
Applied Mathematics and Computation, Volume 322, April 2018, Pages 111–122
16 Pages Posted: 26 Sep 2016 Last revised: 25 Jul 2018
Date Written: September 23, 2016
Abstract
We study an expansion of the cumulative distribution function of the standard normal random variable that results in a family of closed form approximations that converge at 0. One member of the family that has only five explicit constants offers the absolute error of 5.79 10^{-6} across the entire range of real numbers. With its simple form and applicability for all real numbers, our approximation surpasses either in computational efficiency or in relative error, and most often in both, other approximation formulas based on numerical algorithms or ad-hoc approximations. An extensive overview and classification of the existing approximations from the literature is included.
Keywords: Standard Normal CDF, Numerical Approximation
JEL Classification: C19, C60, C63
Suggested Citation: Suggested Citation
