Enhancing the Accuracy of Standard Normal Distribution Approximations

  • Omar Eidous Department of Statistics, Yarmouk University, Irbid (21163), Jordan
  • Loai Alzoubi Department of Mathematics, Al al-Bayt University, Mafraq (25113), Jordan
  • Ahmad Hanandeh Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia
DOI: https://doi.org/10.19139/soic-2310-5070-3116
Keywords: Normal distribution, Approximations, Cumulative distribution function, Maximum absolute error, Mean absolute error

Abstract

In this paper, we introduce a novel approximation for the standard normal distribution function, significantly improving its accuracy. Using the maximum absolute error (Max-AE) and mean absolute error (MAE) as metrics, our approximation achieves a Max-AE of 2.95 × 10−5, outperforming most existing methods. Additionally, we present an approximation for the inverse normal distribution, showing its superiority over many current models. Numerical comparisons validate the efficiency of our methods, making them applicable in fields like statistical analysis, machine learning, and financial modeling.
Published
2026-01-24
How to Cite
Eidous, O., Alzoubi, L., & Hanandeh, A. (2026). Enhancing the Accuracy of Standard Normal Distribution Approximations. Statistics, Optimization & Information Computing, 15(4), 2819-2828. https://doi.org/10.19139/soic-2310-5070-3116
Issue
Vol 15 No 4 (2026)
Section
Research Articles
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