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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: 13 Dec 2017

Ivan Matic

CUNY Baruch College

Rados Radoicic

Baruch College, City University of New York

Dan Stefanica

Baruch College, City University of New York

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

Matic, Ivan and Radoicic, Rados and Stefanica, Dan, A Sharp Polya-Based Approximation to the Normal CDF (September 23, 2016). Applied Mathematics and Computation, Volume 322, April 2018, Pages 111–122. Available at SSRN: https://ssrn.com/abstract=2842681 or http://dx.doi.org/10.2139/ssrn.2842681

Ivan Matic

CUNY Baruch College ( email )

17 Lexington Avenue
New York, NY 10021
United States

Rados Radoicic

Baruch College, City University of New York ( email )

17 Lexington Avenue
New York, NY 10021
United States

Dan Stefanica (Contact Author)

Baruch College, City University of New York ( email )

One Bernard Baruch Way
New York, NY 10010
United States

HOME PAGE: http://mfe.baruch.cuny.edu/dan-stefanica

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