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A new very simply explicitly invertible approximation for the standard normal cumulative distribution function
Publikationstyp
Journal Article
Date Issued
2022-04-15
Sprache
English
Author(s)
Journal
Volume
7
Issue
7
Start Page
11635
End Page
11646
Citation
Aims Mathematics 7 (7): 11635-11646 (2022)
Publisher DOI
Scopus ID
Publisher
AIMS Press
This paper proposes a new very simply explicitly invertible function to approximate the standard normal cumulative distribution function (CDF). The new function was fit to the standard normal CDF using both MATLAB's Global Optimization Toolbox and the BARON software package. The results of three separate fits are presented in this paper. Each fit was performed across the range 0 ≤ z ≤ 7 and achieved a maximum absolute error (MAE) superior to the best MAE reported for previously published very simply explicitly invertible approximations of the standard normal CDF. The best MAE reported from this study is 2.73e–05, which is nearly a factor of five better than the best MAE reported for other published very simply explicitly invertible approximations.
Subjects
Cumulative distribution function
Normal distribution
Optimization
DDC Class
600: Technology