# 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].

### 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.

### 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,
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.

### 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;

You can go up one level to the Python source codes.

Last revised on 23 March 2015.