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<html>
<head>
<title>
ASA226 - CDF of the noncentral Beta Distribution
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
ASA226 <br> CDF of the noncentral Beta Distribution
</h1>
<hr>
<p>
<b>ASA226</b>
is a C++ library which
evaluates the cumulative distribution function (CDF)
of the noncentral Beta Distribution.
</p>
<p>
<b>ASA226</b> is Applied Statistics Algorithm 226. Source code for many
Applied Statistics Algorithms is available through
<a href = "http://lib.stat.cmu.edu/apstat">STATLIB</a>.
</p>
<p>
The program can produce reasonably accurate answers for values
of the noncentrality parameter up to about 100.
</p>
<p>
<i>
Note that an improvement to <b>ASA226</b> was suggested by Frick,
and implemented in the online copy available through STATLIB.
When I run the improved copy, the computation fails. Therefore,
the version I have put together has suppressed the improvement for now
until I can determine the stray minus sign or logic error causing
the problem.
</i>
</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>ASA226</b> is available in
<a href = "../../c_src/asa226/asa226.html">a C version</a> and
<a href = "../../cpp_src/asa226/asa226.html">a C++ version</a> and
<a href = "../../f77_src/asa226/asa226.html">a FORTRAN77 version</a> and
<a href = "../../f_src/asa226/asa226.html">a FORTRAN90 version</a> and
<a href = "../../m_src/asa226/asa226.html">a MATLAB version</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/asa063/asa063.html">
ASA063</a>,
a C++ library which
evaluates the incomplete Beta function.
</p>
<p>
<a href = "../../cpp_src/asa109/asa109.html">
ASA109</a>,
a C++ library which
inverts the incomplete Beta function.
</p>
<p>
<a href = "../../cpp_src/asa310/asa310.html">
ASA310</a>,
a C++ library which
computes the CDF of the noncentral Beta distribution.
</p>
<p>
<a href = "../../cpp_src/beta_nc/beta_nc.html">
BETA_NC</a>,
a C++ library which
evaluates the CDF of the noncentral Beta distribution.
</p>
<p>
<a href = "../../cpp_src/dcdflib/dcdflib.html">
DCDFLIB</a>,
a C++ library which
evaluates and inverts a number of statistical distributions.
</p>
<p>
<a href = "../../cpp_src/gsl/gsl.html">
GSL</a>,
a C++ library which
includes many routines for evaluating
probability distributions.
</p>
<p>
<a href = "../../cpp_src/prob/prob.html">
PROB</a>,
a C++ library which
evaluates and inverts a number of probabilistic distributions.
</p>
<p>
<a href = "../../cpp_src/test_values/test_values.html">
TEST_VALUES</a>,
a C++ library which
contains sample values for a number of distributions.
</p>
<p>
<a href = "../../cpp_src/toms179/toms179.html">
TOMS179</a>,
a C++ library which
evaluates the incomplete Beta function.
</p>
<p>
<a href = "../../f_src/toms708/toms708.html">
TOMS708</a>,
a FORTRAN90 library which
evaluates the incomplete Beta function.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
H Frick,<br>
Algorithm AS R84:
A Remark on Algorithm AS 226:
Computing Noncentral Beta Probabilities,<br>
Applied Statistics,<br>
Volume 39, Number 2, 1990, pages 311-312.
</li>
<li>
Russell Lenth,<br>
Algorithm AS 226:
Computing Noncentral Beta Probabilities,<br>
Applied Statistics,<br>
Volume 36, Number 2, 1987, pages 241-244.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "asa226.cpp">asa226.cpp</a>, the source code.
</li>
<li>
<a href = "asa226.hpp">asa226.hpp</a>, the include file.
</li>
<li>
<a href = "asa226.sh">asa226.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "asa226_prb.cpp">asa226_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "asa226_prb.sh">asa226_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "asa226_prb_output.txt">asa226_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BETA_NONCENTRAL_CDF_VALUES</b> returns some values of the noncentral
Beta CDF.
</li>
<li>
<b>BETAIN</b> computes the incomplete Beta function ratio.
</li>
<li>
<b>BETANC</b> computes the tail of the noncentral Beta distribution.
</li>
<li>
<b>TIMESTAMP</b> prints out the current YMDHMS date as a timestamp.
</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 24 January 2008.
</i>
<!-- John Burkardt -->
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</html>