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Approximations to the Normal Distribution Function and An Extended Table for the Mean Range of the Normal Variables

Author

Listed:
  • Kiani, M
  • Panaretos, J
  • Psarakis, S
  • Saleem, M

Abstract

This article presents a formula and a series for approx¬imating the normal distribution function. Over the whole range of the normal variable z, the proposed formula has the greatest absolute error less than 6.5e - 09, and series has a very high accuracy. We examine the accuracy of our proposed formula and series for various values of z’s. In the sense of accuracy, our formula and series are su¬perior to other formulae and series available in the literature. Based on the proposed formula an extended table for the mean range of the normal variables is established.

Suggested Citation

  • Kiani, M & Panaretos, J & Psarakis, S & Saleem, M, 2008. "Approximations to the Normal Distribution Function and An Extended Table for the Mean Range of the Normal Variables," MPRA Paper 68045, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:68045
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    File URL: https://mpra.ub.uni-muenchen.de/68045/1/Panaretos-JIRSS2008%2857-72%29ft.pdf
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    References listed on IDEAS

    as
    1. Vedder, John D., 1993. "An invertible approximation to the normal distribution function," Computational Statistics & Data Analysis, Elsevier, vol. 16(1), pages 119-123, June.
    2. Robert A. Lew, 1981. "An Approximation to the Cumulative Normal Distribution with Simple Coefficients," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 30(3), pages 299-301, November.
    3. Brent, Richard P., 2004. "Note on Marsaglia's Xorshift Random Number Generators," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i05).
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Ravi Kashyap, 2016. "The Perfect Marriage and Much More: Combining Dimension Reduction, Distance Measures and Covariance," Papers 1603.09060, arXiv.org, revised Jul 2019.
    2. De Schrijver, Steven K. & Aghezzaf, El-Houssaine & Vanmaele, Hendrik, 2014. "Double precision rational approximation algorithm for the inverse standard normal second order loss function," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 247-253.
    3. Kashyap, Ravi, 2021. "Artificial Intelligence: A Child’s Play," Technological Forecasting and Social Change, Elsevier, vol. 166(C).
    4. Kashyap, Ravi, 2019. "The perfect marriage and much more: Combining dimension reduction, distance measures and covariance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).

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    More about this item

    Keywords

    Accuracy; error Function; normal Distribution;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

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