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<html>
<head>
<title>
TOMS179 - Modified Beta Function
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TOMS179 <br> Modified Beta Function
</h1>
<hr>
<p>
<b>TOMS179</b>
is a MATLAB library which
implements ACM TOMS algorithm 179, for evaluating the modified
Beta function.
</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>, many of the early
algorithms are not available. This is one of them. I typed it
in.
</p>
<p>
The original algorithm was published in the Algol language.
Shortly therafter, a distinct FORTRAN77 algorithm was published
as a "remark" to the original algorithm. A few modifications to
the FORTRAN77 program were proposed in a subsequent "remark".
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
[ <i>prob</i>, <i>ier</i> ] = <b>mdbeta</b> ( <i>x</i>, <i>p</i>, <i>q</i> )
</blockquote>
where
<ul>
<li>
<i>x</i> is the point of evaluation;
</li>
<li>
<i>p</i> and <i>q</i> are parameters;
</li>
<li>
<i>prob</i>, (output), is the computed probability;
</li>
<li>
<i>ier</i>, (output), is an error flag.
</li>
</ul>
</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>TOMS179</b> is available in
<a href = "../../c_src/toms179/toms179.html">a C version</a> and
<a href = "../../cpp_src/toms179/toms179.html">a C++ version</a> and
<a href = "../../f77_src/toms179/toms179.html">a FORTRAN77 version</a> and
<a href = "../../f_src/toms179/toms179.html">a FORTRAN90 version</a> and
<a href = "../../m_src/toms179/toms179.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/asa063/asa063.html">
ASA063</a>,
a MATLAB library which
evaluates the incomplete Beta function.
</p>
<p>
<a href = "../../m_src/asa109/asa109.html">
ASA109</a>,
a MATLAB library which
inverts the incomplete Beta function.
</p>
<p>
<a href = "../../m_src/asa226/asa226.html">
ASA226</a>,
a MATLAB library which
evaluates the CDF of the noncentral Beta distribution.
</p>
<p>
<a href = "../../m_src/asa310/asa310.html">
ASA310</a>,
a MATLAB library which
computes the CDF of the noncentral Beta distribution.
</p>
<p>
<a href = "../../m_src/beta_nc/beta_nc.html">
BETA_NC</a>,
a MATLAB library which
evaluates the CDF of the noncentral Beta distribution.
</p>
<p>
<a href = "../../f_src/dcdflib/dcdflib.html">
DCDFLIB</a>,
a FORTRAN90 library which
contains routines which evaluate a number of probability density
functions, including one based on the Beta function.
</p>
<p>
<a href = "../../m_src/prob/prob.html">
PROB</a>,
a MATLAB library which
contains routines which evaluate a number of probability density
functions, including one based on the Beta function.
</p>
<p>
<a href = "../../m_src/test_values/test_values.html">
TEST_VALUES</a>,
a MATLAB library which
contains routines which return sample values of various functions,
including the modified beta function, and the logarithm of the
gamma 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>
Nancy Bosten, EL Battiste,<br>
Remark on Algorithm 179:
Incomplete Beta Ratio,<br>
Communications of the ACM,<br>
Volume 17, Number 3, March 1974, pages 156-157.
</li>
<li>
William Cody, Kenneth Hillstrom,<br>
Chebyshev Approximations for the Natural Logarithm of the
Gamma Function,<br>
Mathematics of Computation,<br>
Volume 21, Number 98, April 1967, pages 198-203.
</li>
<li>
John Hart, Ward Cheney, Charles Lawson, Hans Maehly,
Charles Mesztenyi, John Rice, Henry Thacher,
Christoph Witzgall,<br>
Computer Approximations,<br>
Wiley, 1968,<br>
LC: QA297.C64.
</li>
<li>
Oliver Ludwig,<br>
Algorithm 179:
Incomplete Beta Ratio,<br>
Communications of the ACM,<br>
Volume 6, Number 6, June 1963, page 314.
</li>
<li>
Malcolm Pike, Jennie SooHoo,<br>
Remark on Algorithm 179:
Incomplete Beta Ratio,<br>
ACM Transactions on Mathematical Software,<br>
Volume 2, Number 2, June 1976, pages 207-208.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "alogam.m">alogam.m</a>
calculates the natural logarithm of GAMMA ( X ).
</li>
<li>
<a href = "beta_cdf_values.m">beta_cdf_values.m</a>
returns some values of the Beta CDF.
</li>
<li>
<a href = "gamma_log_values.m">gamma_log_values.m</a>
returns some values of the Log Gamma function.
</li>
<li>
<a href = "mdbeta.m">mdbeta.m</a>
evaluates the incomplete beta function.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>
<b>TIMESTAMP</b> prints out the current YMDHMS date as a timestamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "toms179_test.m">toms179_test.m</a>,
a sample calling program.
</li>
<li>
<a href = "toms179_test01.m">toms179_test01.m</a>,
tests ALOGAM.
</li>
<li>
<a href = "toms179_test02.m">toms179_test02.m</a>,
tests MDBETA.
</li>
<li>
<a href = "toms179_test_output.txt">toms179_test_output.txt</a>,
the output from a run of the sample program.
</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 30 January 2008.
</i>
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