truncated_normal_rule

truncated_normal_rule, a Python code 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 MIT license

Languages:

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

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truncated_normal, a Python code 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:

• truncated_normal_rule.py, the source code.
• truncated_normal_rule.sh, runs all the tests.
• truncated_normal_rule.txt, the output file.

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;

• option0_r.txt, the output "region" file.
• option0_w.txt, the output "weight" file.
• option0_x.txt, the output "point" file.

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;

• option1_r.txt, the output "region" file.
• option1_w.txt, the output "weight" file.
• option1_x.txt, the output "point" file.

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;

• option2_r.txt, the output "region" file.
• option2_w.txt, the output "weight" file.
• option2_x.txt, the output "point" file.

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;

• option3_r.txt, the output "region" file.
• option3_w.txt, the output "weight" file.
• option3_x.txt, the output "point" file.