Inverse of Normal Cumulative Density Function (CDF)

ASA241 is a Python library which computes the inverse of the Normal Cumulative Density Function (CDF), by Michael Wichura;

ASA241 is Applied Statistics Algorithm 241. Source code for many Applied Statistics Algorithms is available through STATLIB.

The library includes two routines, R4_NORMAL_01_CDF_INVERSE, and R8_NORMAL_01_CDF_INVERSE, suitable for single or double precision arithmetic calculations.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


ASA241 is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

PROB, a Python library which contains routines for evaluating and inverting the normal CDF, and many other distributions.

TEST_VALUES, a Python library which contains routines that store selected values of the normal CDF, and many other statistical distributions.


Original FORTRAN77 version by Michael Wichura; Python version by John Burkardt.


  1. Michael Wichura,
    Algorithm AS 241: The Percentage Points of the Normal Distribution,
    Applied Statistics,
    Volume 37, Number 3, 1988, pages 477-484.

Source Code:

Last revised on 09 August 2018.