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<html>
<head>
<title>
ASA310 - CDF of the noncentral Beta distribution
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
ASA310 <br> CDF of the noncentral Beta distribution
</h1>
<hr>
<p>
<b>ASA310</b>
is a C++ library which
computes the cumulative distribution function (CDF) of the
noncentral Beta distribution.
</p>
<p>
<b>ASA310</b> is Applied Statistics Algorithm 310. Source code for many
Applied Statistics Algorithms is available through
<a href = "http://lib.stat.cmu.edu/apstat">STATLIB</a>.
</p>
<hr>
<p>
<b>
Warning:
</b>
<i>
I could not get this algorithm to perform properly until
I had made a number of corrections.
</i>
</p>
<p>
<i>
Note that the printed text of the algorithm, and the online version
distributed by APSTAT, omit a crucial initialization of the variable
S to zero.
<p>
Moreover, there are two typographical errors introduced into the
online version distributed by APSTAT; in both cases a multiplication
symbol became a minus sign.
<p>
Finally, note that the authors of AS 310 invoke AS 226, but specifically
recommend that the changes submitted by Frick NOT be included.
The version of AS 226 distributed by APSTAT includes the Frick changes;
the version of AS310 distributed by APSTAT includes this copy of AS 226,
and hence the changes suggested by Frick.
</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>ASA310</b> is available in
<a href = "../../c_src/asa310/asa310.html">a C version</a> and
<a href = "../../cpp_src/asa310/asa310.html">a C++ version</a> and
<a href = "../../f77_src/asa310/asa310.html">a FORTRAN77 version</a> and
<a href = "../../f_src/asa310/asa310.html">a FORTRAN90 version</a> and
<a href = "../../m_src/asa310/asa310.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/asa226/asa226.html">
ASA226</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 = "../../f77_src/toms708/toms708.html">
TOMS708</a>,
a FORTRAN77 library which
evaluates the incomplete Beta function.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
R Chattamvelli, R Shanmugam,<br>
Algorithm AS 310:
Computing the Non-central Beta Distribution Function,<br>
Applied Statistics,<br>
Volume 46, Number 1, 1997, pages 146-156.
</li>
<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 = "asa310.cpp">asa310.cpp</a>, the source code.
</li>
<li>
<a href = "asa310.hpp">asa310.hpp</a>, the include file.
</li>
<li>
<a href = "asa310.sh">asa310.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "asa310_prb.cpp">asa310_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "asa310_prb.sh">asa310_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "asa310_prb_output.txt">asa310_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>ALNORM</b> computes the cumulative density of the standard normal distribution.
</li>
<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>GAMMAD</b> computes the Incomplete Gamma Integral
</li>
<li>
<b>NCBETA</b> computes the noncentral Beta CDF.
</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 03 February 2008.
</i>
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