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

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Author Info
Chokri Dridi

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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.

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Publisher Info
Paper provided by EconWPA in its series Computational Economics with number 0212001.

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Length: 13 pages
Date of creation: 27 Dec 2002
Date of revision: 07 Jan 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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Related research
Keywords: C/C++ Gauss-Legendre Quadarture Normal distribution Numerical Integration Rational fraction approximations Software;

Find related papers by JEL classification:
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - 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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  1. John Geweke, 1995. "Monte Carlo simulation and numerical integration," Staff Report 192, Federal Reserve Bank of Minneapolis. [Downloadable!]
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