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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 MATLAB 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 = "../../m_src/owens/owens.html">
OWENS</a>,
a MATLAB library which
evaluates Owen's T function.
</p>
<p>
<a href = "../../m_src/prob/prob.html">
PROB</a>,
a MATLAB library which
contains a
number of routines for evaluating cumulative distribution functions.
</p>
<p>
<a href = "../../m_src/test_values/test_values.html">
TEST_VALUES</a>,
a MATLAB 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 = "bivnor.m">bivnor.m</a>
computes the bivariate CDF.
</li>
<li>
<a href = "bivariate_normal_cdf_values.m">bivariate_normal_cdf_values.m</a>,
returns some values of the bivariate normal CDF.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
returns the YMDHMS date as a timestamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "toms462_test.m">toms462_test.m</a>,
calls all the tests.
</li>
<li>
<a href = "toms462_test_output.txt">toms462_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "toms462_test01.m">toms462_test01.m</a>,
makes a quick check against data accurate to three digits.
</li>
<li>
<a href = "toms462_test02.m">toms462_test02.m</a>,
compares the computation to a set of tabulated data.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 13 April 2012.
</i>
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</body>
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</html>