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New Tightness Lower and Upper Bounds for the Standard Normal Distribution Function and Related Functions
  • Omar Eidous
Omar Eidous
Yarmouk University Faculty of Sciences

Corresponding Author:[email protected]

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Most researches interested in finding the bounds of the cumulative standard normal distribution Φ(x) are not tight for all positive values of the argument x. This paper mainly proposes new simple lower and upper bounds for Φ(x). Over the whole range of the positive argument x, the maximum absolute difference between the proposed lower bound and Φ(x) is less than 3×〖10〗^(-4), while it is less than 4.8×〖10〗^(-4) between the proposed upper bound and Φ(x). Numerical comparisons have been made between the proposed bounds and some of the other existing bounds, which showed that the proposed bounds are more compact than most alternative bounds found in the literature.
13 Jul 2022Submitted to Mathematical Methods in the Applied Sciences
14 Jul 2022Submission Checks Completed
14 Jul 2022Assigned to Editor
27 Jul 2022Reviewer(s) Assigned
20 Jan 2023Review(s) Completed, Editorial Evaluation Pending
27 Jan 2023Editorial Decision: Revise Minor
02 Feb 20231st Revision Received
02 Feb 2023Submission Checks Completed
02 Feb 2023Assigned to Editor
02 Feb 2023Review(s) Completed, Editorial Evaluation Pending
07 Feb 2023Reviewer(s) Assigned
23 Apr 2023Editorial Decision: Accept