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 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:

• truncated_normal_rule.py, the main program, which can interact with the user to compute a quadrature rule for the truncated normal distribution.
• i4_uniform_ab.py, returns a randomly selected integer between A and B.
• moment_method.py, computes a quadrature rule by the method of moments.
• normal_01_cdf.py, evaluates the Normal 01 CDF.
• normal_01_moment.py, evaluates a moment of the Normal 01 distribution.
• normal_01_pdf.py, evaluates the Normal 01 PDF.
• normal_MS_moment.py, evaluates a moment of the Normal MS distribution.
• r8_choose.py, computes the binomial coefficient C(N,K) as an R8.
• r8_factorial.py, computes the factorial of N.
• r8_factorial_values.py, returns selected values of the factorial function.
• r8_factorial2.py, computes the double factorial function.
• r8_factorial2_values.py, returns selected values of the double factorial function.
• r8_gamma_log.py, returns the logarithm of the gamma function.
• r8_huge.py, returns a very large R8.
• r8_mop.py, returns the I-th power of -1 as an R8.
• r8mat_print.py, prints an R8MAT.
• r8mat_print_some.py, prints some of an R8MAT.
• r8mat_write.py, writes an R8MAT file.
• r8vec_print.py, prints an R8VEC.
• rule_write.py, writes a quadrature rule to a file.
• timestamp.py, prints the current YMDHMS date as a time stamp.
• truncated_normal_a_moment.py, moments of the lower truncated Normal PDF.
• truncated_normal_ab_moment.py, moments of the truncated Normal PDF.
• truncated_normal_b_moment.py, moments of the upper truncated Normal PDF.

Examples and Tests:

• truncated_normal_rule_test.py, a program that calls all the tests.
• truncated_normal_rule_test.sh, a BASH shell script that executes the test program.
• truncated_normal_rule_test.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.

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