A logistic approximation to the cumulative normal distribution

Bowling, Shannon R. ^[1] ; Khasawneh, Mohammad T. ^[2] ; Kaewkuekool, Sittichai ^[4] ; Cho, Byung Rae ^[3]
1. [1] Old Dominion University
  
  Old Dominion University
  
  Estados Unidos
2. [2] State University of New York
  
  State University of New York
  
  City of Albany, Estados Unidos
3. [3] Clemson University
  
  Clemson University
  
  Estados Unidos
4. [4] King Mongkut’s University of Technology Thonburi
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Localización: Journal of Industrial Engineering and Management, ISSN-e 2013-0953, Vol. 2, Nº. 1, 2009, págs. 114-127
Idioma: inglés
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Resumen
- 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.