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toms462.html
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<html>
<head>
<title>
TOMS462 - Bivariate Normal Distribution
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TOMS462 <br> Bivariate Normal Distribution
</h1>
<hr>
<p>
<b>TOMS462</b>
is a C++ library which
evaluates the upper right tail of the bivariate normal distribution; that is,
the probability that normal variables X and Y with correlation R will
satisfy H <= X and K <= Y.
</p>
<p>
While the text of many ACM TOMS algorithms is available online
through ACM:
<a href = "http://www.acm.org/pubs/calgo/">
http://www.acm.org/pubs/calgo</a>
or NETLIB:
<a href = "http://www.netlib.org/toms/index.html">
http://www.netlib.org/toms/index.html</a>, most of the early
algorithms are not available. This is one of them. I typed it
in.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<dl>
<dt>
value = <b>bivnor ( ah, ak, r )</b>
</dt>
<dd>
computes <b>VALUE</b>, the probability that two variables,
<i>X</i> and <i>Y</i> related by a bivariate normal distribution
with correlation <b>R</b>, satisfy <b>AH</b> <= <i>X</i> and
<b>AK</b> <= <i>Y</i>.
</dd>
</dl>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and 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>TOMS462</b> is available in
<a href = "../../c_src/toms462/toms462.html">a C version</a> and
<a href = "../../cpp_src/toms462/toms462.html">a C++ version</a> and
<a href = "../../f77_src/toms462/toms462.html">a FORTRAN77 version</a> and
<a href = "../../f_src/toms462/toms462.html">a FORTRAN90 version</a> and
<a href = "../../m_src/toms462/toms462.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/owens/owens.html">
OWENS</a>,
a C++ library which
evaluates Owen's T function.
</p>
<p>
<a href = "../../cpp_src/prob/prob.html">
PROB</a>,
a C++ library which
contains a
number of routines for evaluating cumulative distribution functions.
</p>
<p>
<a href = "../../cpp_src/test_values/test_values.html">
TEST_VALUES</a>,
a C++ library which
supplies test values of various mathematical functions.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Thomas Donnelly,<br>
Algorithm 462: Bivariate Normal Distribution,<br>
Communications of the ACM,<br>
October 1973, Volume 16, Number 10, page 638.
</li>
<li>
Donald Owen,<br>
Tables for Computing Bivariate Normal Probabilities,<br>
Annals of Mathematical Statistics,<br>
Volume 27, Number 4, pages 1075-1090, December 1956.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "toms462.cpp">toms462.cpp</a>, the source code.
</li>
<li>
<a href = "toms462.hpp">toms462.hpp</a>, the include file.
</li>
<li>
<a href = "toms462.sh">toms462.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "toms462_prb.cpp">toms462_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "toms462_prb.sh">toms462_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "toms462_prb_output.txt">toms462_prb_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BIVARIATE_NORMAL_CDF_VALUES</b> returns some values of the bivariate normal CDF.
</li>
<li>
<b>BIVNOR</b> computes the bivariate normal CDF.
</li>
<li>
<b>GAUSS</b> returns the area of the lower tail of the normal curve.
</li>
<li>
<b>R8_ABS</b> returns the absolute value of an R8.
</li>
<li>
<b>R8_MAX</b> returns the maximum of two R8's.
</li>
<li>
<b>R8_MIN</b> returns the minimum of two R8's.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</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 13 April 2012.
</i>
<!-- John Burkardt -->
</body>
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</html>