TRUNCATED_NORMAL_RULE
Quadrature Rule for Truncated Normal Distribution

TRUNCATED_NORMAL_RULE, a FORTRAN77 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:

CLENSHAW_CURTIS_RULE, a FORTRAN77 program which defines a Clenshaw Curtis quadrature rule.

LAGUERRE_RULE, a FORTRAN77 program which can compute and print a Gauss-Laguerre quadrature rule for estimating the integral of a function with density exp(-x) over the interval [0,+oo).

PATTERSON_RULE, a FORTRAN77 program which returns the points and weights of a 1D Gauss-Patterson quadrature rule of order 1, 3, 7, 15, 31, 63, 127, 255 or 511.

QUADRULE, a FORTRAN77 library which defines 1-dimensional quadrature rules.

TRUNCATED_NORMAL, a FORTRAN77 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:

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

Source Code:

truncated_normal_rule.f, the source code.
truncated_normal_rule.sh, BASH commands to compile the source code.

Examples and Tests:

"OPTION0" computes a quadrature rule for the normal distribution, n = 5, mu = 1.0, sigma = 2.0;

option0_input.txt, the input file.
option0_r.txt, the output "region" file.
option0_w.txt, the output "weight" file.
option0_x.txt, the output "point" file.

"OPTION1" computes a quadrature rule for the lower truncated normal distribution, n = 9, mu = 2.0, sigma = 0.5, a = 0.0;

option1_input.txt, the input file.
option1_r.txt, the output "region" file.
option1_w.txt, the output "weight" file.
option1_x.txt, the output "point" file.

"OPTION2" computes a quadrature rule for the upper truncated normal distribution, n = 9, mu = 2.0, sigma = 0.5, b = 3.0;

option2_input.txt, the input file.
option2_r.txt, the output "region" file.
option2_w.txt, the output "weight" file.
option2_x.txt, the output "point" file.

"OPTION3" 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_input.txt, the input file.
option3_r.txt, the output "region" file.
option3_w.txt, the output "weight" file.
option3_x.txt, the output "point" file.

List of Routines:

MAIN is the main program for TRUNCATED_NORMAL_RULE.
CH_CAP capitalizes a single character.
CH_EQI is a case insensitive comparison of two characters for equality.
CH_TO_DIGIT returns the value of a base 10 digit.
GET_UNIT returns a free FORTRAN unit number.
JACOBI_EIGENVALUE carries out the Jacobi eigenvalue iteration.
MOMENT_METHOD computes a quadrature rule by the method of moments.
MOMENTS_NORMAL returns moments of the standard Normal distribution.
MOMENTS_TRUNCATED_NORMAL_AB: moments of truncated Normal distribution.
MOMENTS_TRUNCATED_NORMAL_A: moments of lower truncated Normal distribution.
MOMENTS_TRUNCATED_NORMAL_B: moments of upper truncated Normal distribution.
NORMAL_01_CDF evaluates the Normal 01 CDF.
NORMAL_01_PDF evaluates the Normal 01 PDF.
R8_CHOOSE computes the binomial coefficient C(N,K) as an R8.
R8_FACTORIAL computes the factorial of N.
R8_FACTORIAL2 computes the double factorial function.
R8_HUGE returns a very large R8.
R8_MOP returns the I-th power of -1 as an R8.
R8MAT_CHOLESKY_FACTOR_UPPER: upper Cholesky factor of a symmetric matrix.
R8MAT_PRINT prints an R8MAT.
R8MAT_PRINT_SOME prints some of an R8MAT.
R8MAT_WRITE writes an R8MAT file.
R8VEC_PRINT prints an R8VEC.
RULE_WRITE writes a quadrature rule to a file.
S_TO_I4 reads an I4 from a string.
S_TO_R8 reads an R8 value from a string.
TIMESTAMP prints the current YMDHMS date as a time stamp.
TRUNCATED_NORMAL_AB_MOMENT: moments of the truncated Normal PDF.
TRUNCATED_NORMAL_A_MOMENT: moments of the lower truncated Normal PDF.
TRUNCATED_NORMAL_B_MOMENT: moments of the upper truncated Normal PDF.

You can go up one level to the FORTRAN77 source codes.

Last revised on 20 September 2013.

TRUNCATED_NORMAL_RULE Quadrature Rule for Truncated Normal Distribution