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New approximations for standard normal distribution function

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  • Omar M. Eidous
  • Rima Abu-Shareefa

Abstract

This article proposes nine new approximations for the standard normal cumulative distribution function Φz. In addition, it collects most of the approximations existing in the literature. The accuracy of the proposed approximations is evaluated by using the maximum absolute error and the mean absolute error. The maximum absolute errors fall between 0.0422613 × 10−6 and 950.55 × 10−6, which indicates high accuracy for some of them. A comparison study between the different existing approximations and the proposed approximations is also accomplished.

Suggested Citation

  • Omar M. Eidous & Rima Abu-Shareefa, 2020. "New approximations for standard normal distribution function," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(6), pages 1357-1374, March.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:6:p:1357-1374
    DOI: 10.1080/03610926.2018.1563166
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    Cited by:

    1. Michele Mininni & Giuseppe Orlando & Giovanni Taglialatela, 2021. "Challenges in approximating the Black and Scholes call formula with hyperbolic tangents," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 73-100, June.

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