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<html>
<head>
<title>
TOMS708 - Incomplete Beta Function Ratios
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TOMS708 <br> Incomplete Beta Function Ratios
</h1>
<hr>
<p>
<b>TOMS708</b>
is a FORTRAN90 library which
computes the Incomplete Beta Function ratio
<pre><b>
I<sub>x</sub>(a,b)
</b></pre>
</p>
<p>
<i>
11 January 2006: Thanks to Ian Smith for pointing out that my
earlier difficulties with this program were caused simply by
using the wrong set of machine constants!
</i>
</p>
<p>
The original, true, correct version of ACM TOMS Algorithm 708
is available
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>.
</p>
<p>
The version displayed here has been converted to FORTRAN90,
and other internal changes have been made to suit me.
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TOMS708</b> is available in
<a href = "../../java_src/toms708/toms708.html">a JAVA version</a> and
<a href = "../../f77_src/toms708/toms708.html">a FORTRAN77 version</a> and
<a href = "../../f_src/toms708/toms708.html">a FORTRAN90 version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/asa063/asa063.html">
ASA063</a>
is a FORTRAN90 library which
evaluates the incomplete Beta function.
</p>
<p>
<a href = "../../f_src/asa109/asa109.html">
ASA109</a>
is a FORTRAN90 library which
inverts the incomplete Beta function.
</p>
<p>
<a href = "../../f_src/asa226/asa226.html">
ASA226</a>
is a FORTRAN90 library which
computes the CDF of the noncentral Beta distribution.
</p>
<p>
<a href = "../../f_src/asa310/asa310.html">
ASA310</a>
is a FORTRAN90 library which
computes the CDF of the noncentral Beta distribution.
</p>
<p>
<a href = "../../f_src/beta_nc/beta_nc.html">
BETA_NC</a>
is a FORTRAN90 library which
evaluates the CDF of the noncentral Beta distribution.
</p>
<p>
<a href = "../../f_src/test_values/test_values.html">
TEST_VALUES</a>
is a FORTRAN90 library which
stores a few values of various mathematical functions.
</p>
<p>
<a href = "../../f_src/toms179/toms179.html">
TOMS179</a>
is a FORTRAN90 library which
approximates the incomplete Beta function.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Armido Didonato, Alfred Morris, Jr,<br>
Algorithm 708:
Significant Digit Computation of the Incomplete Beta
Function Ratios,<br>
ACM Transactions on Mathematical Software,<br>
Volume 18, Number 3, pages 360-373, 1992.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "toms708.f90">toms708.f90</a>,
the source code;
</li>
<li>
<a href = "toms708.sh">toms708.sh</a>,
commands to compile the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "toms708_prb.f90">toms708_prb.f90</a>,
a sample calling program;
</li>
<li>
<a href = "toms708_prb.sh">toms708_prb.sh</a>,
commands to compile, link and run the test program;
</li>
<li>
<a href = "toms708_prb_output.txt">toms708_prb_output.txt</a>,
output from a run of the test program;
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>ALGDIV</b> computes ln(gamma(b)/gamma(a+b)) when 8 <= B.
</li>
<li>
<b>ALNREL</b> evaluates the function ln(1 + a).
</li>
<li>
<b>APSER</b> yields the incomplete beta ratio i(sub(1-x))(b,a) for
</li>
<li>
<b>BASYM</b> uses an asymptotic expansion for Ix(A,B) for large A and B.
</li>
<li>
<b>BCORR</b> evaluates del(a0) + del(b0) - del(a0 + b0) where
</li>
<li>
<b>BETA_INC_VALUES</b> returns some values of the incomplete Beta function.
</li>
<li>
<b>BETA_LOG_VALUES</b> returns some values of the Beta function for testing.
</li>
<li>
<b>BETALN</b> evaluates the logarithm of the Beta function.
</li>
<li>
<b>BFRAC</b> uses a continued fraction expansion for ix(a,b) when a,b .gt. 1.
</li>
<li>
<b>BGRAT</b> uses an asymptotic expansion for Ix(a,b) when a is larger than b.
</li>
<li>
<b>BPSER</b> uses the power series expansion for evaluating ix(a,b) when b <= 1
</li>
<li>
<b>BRATIO</b> evaluates the incomplete beta function Ix(A,B).
</li>
<li>
<b>BRCMP1</b> evaluates exp(mu) * (x**a*y**b/beta(a,b)).
</li>
<li>
<b>BRCOMP</b> evaluates X**a * y**b / beta(a,b).
</li>
<li>
<b>BUP</b> evaluates ix(a,b) - ix(a+n,b) where n is a positive integer.
</li>
<li>
<b>ERFC1</b> evaluates the complementary error function
</li>
<li>
<b>ERF</b> evaluates the real error function.
</li>
<li>
<b>ERF_VALUES</b> returns some values of the ERF or "error" function for testing.
</li>
<li>
<b>ESUM</b> evaluates exp(mu + x).
</li>
<li>
<b>EXPARG</b> reports the largest safe arguments for EXP(X).
</li>
<li>
<b>FPSER</b> evaluates Ix(A,B) for small B and X <= 0.5.
</li>
<li>
<b>GAM1</b> computes 1/gamma(a+1) - 1 for -0.5 <= a <= 1.5
</li>
<li>
<b>GAMLN1</b> evaluates ln(gamma(1 + a)) for -0.2 <= A <= 1.25
</li>
<li>
<b>GAMLN</b> evaluates ln(gamma(a)) for positive A.
</li>
<li>
<b>GAMMA_INC_VALUES</b> returns some values of the incomplete Gamma function.
</li>
<li>
<b>GAMMA_LOG_VALUES</b> returns some values of the Log Gamma function for testing.
</li>
<li>
<b>GRAT1</b> evaluates the incomplete Gamma ratio functions P(A,X) and Q(A,X).
</li>
<li>
<b>GSUMLN</b> evaluates the function Log ( Gamma ( A + B ) ) in a special range.
</li>
<li>
<b>IPMPAR</b> provides the integer machine constants for the computer
</li>
<li>
<b>PSI</b> evaluates the Psi or Digamma function.
</li>
<li>
<b>PSI_VALUES</b> returns some values of the Psi or Digamma function for testing.
</li>
<li>
<b>REXP</b> evaluates the function Exp(X) - 1.
</li>
<li>
<b>RLOG1</b> evaluates the function X - Log ( 1 + X ).
</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 = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 08 January 2008.
</i>
<!-- John Burkardt -->
</body>
</html>