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A Short Note on the Numerical Approximation of the Standard Normal Cumulative Distribution and Its Inverse

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  • Chokri Dridi

Abstract

We provide computer codes in ANSI-C and Python for a fast and accurate computation of the cumulative distribution function (cdf) of the standard normal distribution and the inverse cdf of the same function. For the cdf we use the 5th order Gauss-Legendre quadrature which gives more accurate results compared to Excel and Matlab. The Inverse cdf is computed using rational fraction approximations and gives a result that is seven-decimal place accurate.

Suggested Citation

  • Chokri Dridi, 2002. "A Short Note on the Numerical Approximation of the Standard Normal Cumulative Distribution and Its Inverse," Computational Economics 0212001, University Library of Munich, Germany, revised 07 Mar 2003.
    • Handle: RePEc:wpa:wuwpco:0212001
    Note: Type of Document - ; pages: 13 ; figures: included. cdf.c : Is ANSI-C code to compute the cdf of standard normal dist. using a composite fifth-order Gauss-Legendre quadrature cdf-GL.py : same as cdf.c except the code is written in Python cdf.py : Python code to compute the cdf using rational fraction approximations invcdf.py : Python code to compute the inverse cdf using rational fraction approximations. ftp://wueconb.wustl.edu/econ-wp/prog/papers/0212/0212001.zip
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    References listed on IDEAS

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    1. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    2. Geweke, John, 1996. "Monte carlo simulation and numerical integration," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 15, pages 731-800, Elsevier.
    3. R. E. Odeh & J. O. Evans, 1974. "The Percentage Points of the Normal Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 23(1), pages 96-97, March.
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    More about this item

    Keywords

    C/C++ Gauss-Legendre Quadarture Normal distribution Numerical Integration Rational fraction approximations Software;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • C89 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other

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