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<html>
<head>
<title>
TRUNCATED_NORMAL_RULE - Quadrature Rule for Truncated Normal Distribution
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TRUNCATED_NORMAL_RULE <br> Quadrature Rule for Truncated Normal Distribution
</h1>
<hr>
<p>
<b>TRUNCATED_NORMAL_RULE</b>,
a C++ 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].
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files made available on this
web page are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TRUNCATED_NORMAL_RULE</b> is available in
<a href = "../../c_src/truncated_normal_rule/truncated_normal_rule.html">a C version</a> and
<a href = "../../cpp_src/truncated_normal_rule/truncated_normal_rule.html">a C++ version</a> and
<a href = "../../f77_src/truncated_normal_rule/truncated_normal_rule.html">a FORTRAN77 version</a> and
<a href = "../../f_src/truncated_normal_rule/truncated_normal_rule.html">a FORTRAN90 version</a> and
<a href = "../../m_src/truncated_normal_rule/truncated_normal_rule.html">a MATLAB version</a> and
<a href = "../../py_src/truncated_normal_rule/truncated_normal_rule.html">a Python version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/chebyshev1_rule/chebyshev1_rule.html">
CHEBYSHEV1_RULE</a>,
a C++ program which
can compute and print a Gauss-Chebyshev type 1 quadrature rule.
</p>
<p>
<a href = "../../cpp_src/chebyshev2_rule/chebyshev2_rule.html">
CHEBYSHEV2_RULE</a>,
a C++ program which
can compute and print a Gauss-Chebyshev type 2 quadrature rule.
</p>
<p>
<a href = "../../cpp_src/clenshaw_curtis_rule/clenshaw_curtis_rule.html">
CLENSHAW_CURTIS_RULE</a>,
a C++ program which
defines a Clenshaw Curtis quadrature rule.
</p>
<p>
<a href = "../../cpp_src/gegenbauer_rule/gegenbauer_rule.html">
GEGENBAUER_RULE</a>,
a C++ program which
can compute and print a Gauss-Gegenbauer quadrature rule.
</p>
<p>
<a href = "../../cpp_src/gen_hermite_rule/gen_hermite_rule.html">
GEN_HERMITE_RULE</a>,
a C++ program which
can compute and print a generalized Gauss-Hermite quadrature rule.
</p>
<p>
<a href = "../../cpp_src/gen_laguerre_rule/gen_laguerre_rule.html">
GEN_LAGUERRE_RULE</a>,
a C++ program which
can compute and print a generalized Gauss-Laguerre quadrature rule.
</p>
<p>
<a href = "../../cpp_src/hermite_rule/hermite_rule.html">
HERMITE_RULE</a>,
a C++ program which
can compute and print a Gauss-Hermite quadrature rule.
</p>
<p>
<a href = "../../cpp_src/jacobi_rule/jacobi_rule.html">
JACOBI_RULE</a>,
a C++ program which
can compute and print a Gauss-Jacobi quadrature rule.
</p>
<p>
<a href = "../../cpp_src/laguerre_rule/laguerre_rule.html">
LAGUERRE_RULE</a>,
a C++ program which
can compute and print a Gauss-Laguerre quadrature rule.
</p>
<p>
<a href = "../../cpp_src/legendre_rule/legendre_rule.html">
LEGENDRE_RULE</a>,
a C++ program which
can compute and print a Gauss-Legendre quadrature rule.
</p>
<p>
<a href = "../../cpp_src/line_felippa_rule/line_felippa_rule.html">
LINE_FELIPPA_RULE</a>,
a C++ library which
returns the points and weights of a Felippa quadrature rule
over the interior of a line segment in 1D.
</p>
<p>
<a href = "../../cpp_src/patterson_rule/patterson_rule.html">
PATTERSON_RULE</a>,
a C++ program which
computes a Gauss-Patterson quadrature rule.
</p>
<p>
<a href = "../../cpp_src/quadrule/quadrule.html">
QUADRULE</a>,
a C++ library which
defines 1-dimensional quadrature rules.
</p>
<p>
<a href = "../../cpp_src/truncated_normal/truncated_normal.html">
TRUNCATED_NORMAL</a>,
a C++ 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.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Gene Golub, John Welsch,<br>
Calculation of Gaussian Quadrature Rules,<br>
Mathematics of Computation,<br>
Volume 23, Number 106, April 1969, pages 221-230.
</li>
<li>
Norman Johnson, Samuel Kotz, Narayanaswamy Balakrishnan,<br>
Continuous Univariate Distributions,<br>
Second edition,<br>
Wiley, 1994,<br>
ISBN: 0471584940,<br>
LC: QA273.6.J6.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "truncated_normal_rule.cpp">truncated_normal_rule.cpp</a>, the source code.
</li>
<li>
<a href = "truncated_normal_rule.sh">truncated_normal_rule.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
"OPTION0" computes a quadrature rule for the normal distribution,
n = 5, mu = 1.0, sigma = 2.0;
<ul>
<li>
<a href = "option0_input.txt">option0_input.txt</a>,
the input file.
</li>
<li>
<a href = "option0_r.txt">option0_r.txt</a>,
the output "region" file.
</li>
<li>
<a href = "option0_w.txt">option0_w.txt</a>,
the output "weight" file.
</li>
<li>
<a href = "option0_x.txt">option0_x.txt</a>,
the output "point" file.
</li>
</ul>
</p>
<p>
"OPTION1" computes a quadrature rule for the lower truncated normal distribution,
n = 9, mu = 2.0, sigma = 0.5, a = 0.0;
<ul>
<li>
<a href = "option1_input.txt">option1_input.txt</a>,
the input file.
</li>
<li>
<a href = "option1_r.txt">option1_r.txt</a>,
the output "region" file.
</li>
<li>
<a href = "option1_w.txt">option1_w.txt</a>,
the output "weight" file.
</li>
<li>
<a href = "option1_x.txt">option1_x.txt</a>,
the output "point" file.
</li>
</ul>
</p>
<p>
"OPTION2" computes a quadrature rule for the upper truncated normal distribution,
n = 9, mu = 2.0, sigma = 0.5, b = 3.0;
<ul>
<li>
<a href = "option2_input.txt">option2_input.txt</a>,
the input file.
</li>
<li>
<a href = "option2_r.txt">option2_r.txt</a>,
the output "region" file.
</li>
<li>
<a href = "option2_w.txt">option2_w.txt</a>,
the output "weight" file.
</li>
<li>
<a href = "option2_x.txt">option2_x.txt</a>,
the output "point" file.
</li>
</ul>
</p>
<p>
"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;
<ul>
<li>
<a href = "option3_input.txt">option3_input.txt</a>,
the input file.
</li>
<li>
<a href = "option3_r.txt">option3_r.txt</a>,
the output "region" file.
</li>
<li>
<a href = "option3_w.txt">option3_w.txt</a>,
the output "weight" file.
</li>
<li>
<a href = "option3_x.txt">option3_x.txt</a>,
the output "point" file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for TRUNCATED_NORMAL_RULE.
</li>
<li>
<b>JACOBI_EIGENVALUE</b> carries out the Jacobi eigenvalue iteration.
</li>
<li>
<b>MOMENT_METHOD</b> computes a quadrature rule by the method of moments.
</li>
<li>
<b>MOMENTS_NORMAL</b> returns moments of the standard Normal distribution.
</li>
<li>
<b>MOMENTS_TRUNCATED_NORMAL_AB:</b> moments of truncated Normal distribution.
</li>
<li>
<b>MOMENTS_TRUNCATED_NORMAL_A:</b> moments of lower truncated Normal distribution.
</li>
<li>
<b>MOMENTS_TRUNCATED_NORMAL_B:</b> moments of upper truncated Normal distribution.
</li>
<li>
<b>NORMAL_01_CDF</b> evaluates the Normal 01 CDF.
</li>
<li>
<b>NORMAL_01_PDF</b> evaluates the Normal 01 PDF.
</li>
<li>
<b>R8_CHOOSE</b> computes the binomial coefficient C(N,K) as an R8.
</li>
<li>
<b>R8_FACTORIAL</b> computes the factorial of N.
</li>
<li>
<b>R8_FACTORIAL2</b> computes the double factorial function.
</li>
<li>
<b>R8_HUGE</b> returns a very large R8.
</li>
<li>
<b>R8_MOP</b> returns the I-th power of -1 as an R8.
</li>
<li>
<b>R8MAT_CHOLESKY_FACTOR_UPPER:</b> upper Cholesky factor of a symmetric matrix.
</li>
<li>
<b>R8MAT_PRINT</b> prints an R8MAT.
</li>
<li>
<b>R8MAT_PRINT_SOME</b> prints some of an R8MAT.
</li>
<li>
<b>R8MAT_WRITE</b> writes an R8MAT file.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>RULE_WRITE</b> writes a quadrature rule to a file.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRUNCATED_NORMAL_AB_MOMENT:</b> moments of the truncated Normal PDF.
</li>
<li>
<b>TRUNCATED_NORMAL_A_MOMENT:</b> moments of the lower truncated Normal PDF.
</li>
<li>
<b>TRUNCATED_NORMAL_B_MOMENT:</b> moments of the upper truncated Normal PDF.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 20 September 2013.
</i>
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