Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2009; 46(6): 1267-1276

Printed November 1, 2009

https://doi.org/10.4134/JKMS.2009.46.6.1267

Copyright © The Korean Mathematical Society.

Approximation to the cumulative normal distribution using hyperbolic tangent based functions

Beong In Yun

Kunsan National University

Abstract

This paper presents a method for approximation of the standard normal distribution by using hyperbolic tangent based functions. The presented approximate formula for the cumulative distribution depends on one numerical coefficient only, and its accuracy is admissible. Furthermore, in some particular cases, closed forms of inverse formulas are derived. % Numerical results of the present method are compared with those of an existing method.

Keywords: cumulative normal distribution, hyperbolic tangent based function

MSC numbers: 62E17, 65D10

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