A logistic approximation to the cumulative normal distribution

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Publication Details

Author list: Bowling S.R., Khasawneh M.T., Kaewkuekool S., Cho B.R.

Publisher: OmniaScience

Publication year: 2009

Journal: Journal of Industrial Engineering and Management (2013-8423)

Volume number: 2

Issue number: 1

Start page: 114

End page: 127

Number of pages: 14

ISSN: 2013-8423

eISSN: 2013-0953

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-77956622678&doi=10.3926%2fjiem.2009.v2n1.p114-127&partnerID=40&md5=1e97cebd8e8d7b94cc96be33a1793e89

Languages: English-Great Britain (EN-GB)

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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. © Journal of Industrial Engineering and Management, 2009.

Keywords

Logistic, Minimax criteria