TRUNCATED_NORMAL_RULE
Quadrature Rule for Truncated Normal Distribution


TRUNCATED_NORMAL_RULE, a Python program which computes a quadrature rule for a normal probability density function (PDF), sometimes called a Gaussian distribution, that has been truncated to [A,+oo), (-oo,B] or [A,B].

Licensing:

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

Languages:

TRUNCATED_NORMAL_RULE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

DISK_RULE, a Python library which computes quadrature rules over the interior of the general disk in 2D, with radius RC and center (XC,YC).

DISK01_RULE, a Python library which computes quadrature rules over the interior of the unit disk in 2D, with center (0,0) and radius 1.

TRUNCATED_NORMAL, a Python library which works with the truncated normal distribution over [A,B], or [A,+oo) or (-oo,B], returning the probability density function (PDF), the cumulative density function (CDF), the inverse CDF, the mean, the variance, and sample values.

Reference:

  1. Gene Golub, John Welsch,
    Calculation of Gaussian Quadrature Rules,
    Mathematics of Computation,
    Volume 23, Number 106, April 1969, pages 221-230.
  2. Norman Johnson, Samuel Kotz, Narayanaswamy Balakrishnan,
    Continuous Univariate Distributions,
    Second edition,
    Wiley, 1994,
    ISBN: 0471584940,
    LC: QA273.6.J6.

Source Code:

Examples and Tests:

OPTION0_TEST is a test included within the text of truncated_normal_rule.py which computes a quadrature rule for the normal distribution, n = 5, mu = 1.0, sigma = 2.0;

OPTION1_TEST is a test included within the text of truncated_normal_rule.py which computes a quadrature rule for the lower truncated normal distribution, n = 9, mu = 2.0, sigma = 0.5, a = 0.0;

OPTION2_TEST is a test included within the text of truncated_normal_rule.py which computes a quadrature rule for the upper truncated normal distribution, n = 9, mu = 2.0, sigma = 0.5, b = 3.0;

OPTION3_TEST is a test included within the text of truncated_normal_rule.py which computes a quadrature rule for the doubly truncated normal distribution, n = 5, mu = 100.0, sigma = 25.0, a = 50.0, b = 100.0;

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Last revised on 23 March 2015.