Enhancing the Accuracy of Standard Normal Distribution Approximations

Authors

  • 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.

Downloads

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

License

Authors who publish with this journal agree to the following terms:

    1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
    2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
    3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).