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A sharp Pólya-based approximation to the normal cumulative distribution function

Author

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  • Matić, Ivan
  • Radoičić, Radoš
  • Stefanica, Dan

Abstract

We study an expansion of the cumulative distribution function of the standard normal random variable that results in a family of closed form approximations that converge at 0. One member of the family that has only five explicit constants offers the absolute error of 5.79·10−6 across the entire range of real numbers. With its simple form and applicability for all real numbers, our approximation surpasses either in computational efficiency or in relative error, and most often in both, other approximation formulas based on numerical algorithms or ad-hoc approximations. An extensive overview and classification of the existing approximations from the literature is included.

Suggested Citation

  • Matić, Ivan & Radoičić, Radoš & Stefanica, Dan, 2018. "A sharp Pólya-based approximation to the normal cumulative distribution function," Applied Mathematics and Computation, Elsevier, vol. 322(C), pages 111-122.
    • Handle: RePEc:eee:apmaco:v:322:y:2018:i:c:p:111-122
    DOI: 10.1016/j.amc.2017.10.019
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