TOMS179
Modified Beta Function

TOMS179 is a C++ library which implements ACM TOMS algorithm 179, for evaluating the modified Beta function.

While the text of many ACM TOMS algorithms is available online through ACM: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html, many of the early algorithms are not available. This is one of them. I typed it in.

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".

Usage:

prob = mdbeta ( x, p, q, &ier )

• x is the point of evaluation;
• p and q are parameters;
• prob, (output), is the computed probability;
• ier, (output), is an error flag.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

TOMS179 is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

ASA063, a C++ library which evaluates the incomplete Beta function.

ASA109, a C++ library which inverts the incomplete Beta function.

ASA226, a C++ library which evaluates the CDF of the noncentral Beta distribution.

ASA310, a C++ library which computes the CDF of the noncentral Beta distribution.

BETA_NC, a C++ library which evaluates the CDF of the noncentral Beta distribution.

DCDFLIB, a C++ library which contains routines which evaluate a number of probability density functions, including one based on the Beta function.

PROB, a C++ library which contains routines which evaluate a number of probability density functions, including one based on the Beta function.

TEST_VALUES, a C++ library which contains routines which return sample values of various functions, including the modified beta function, and the logarithm of the gamma function.

TOMS708, a FORTRAN90 library which evaluates the incomplete beta function.

Reference:

1. Nancy Bosten, EL Battiste,
   Remark on Algorithm 179: Incomplete Beta Ratio,
   Communications of the ACM,
   Volume 17, Number 3, March 1974, pages 156-157.
2. William Cody, Kenneth Hillstrom,
   Chebyshev Approximations for the Natural Logarithm of the Gamma Function,
   Mathematics of Computation,
   Volume 21, Number 98, April 1967, pages 198-203.
3. John Hart, Ward Cheney, Charles Lawson, Hans Maehly, Charles Mesztenyi, John Rice, Henry Thacher, Christoph Witzgall,
   Computer Approximations,
   Wiley, 1968,
   LC: QA297.C64.
4. Oliver Ludwig,
   Algorithm 179: Incomplete Beta Ratio,
   Communications of the ACM,
   Volume 6, Number 6, June 1963, page 314.
5. Malcolm Pike, Jennie SooHoo,
   Remark on Algorithm 179: Incomplete Beta Ratio,
   ACM Transactions on Mathematical Software,
   Volume 2, Number 2, June 1976, pages 207-208.

Source Code:

• toms179.cpp, the source code.
• toms179.hpp, the include file.
• toms179.sh, commands to compile the source code.

Examples and Tests:

• toms179_prb.cpp, a sample calling program.
• toms179_prb.sh, commands to compile and run the sample program.
• toms179_prb_output.txt, the output from a run of the sample program.

List of Routines:

• ALOGAM calculates the natural logarithm of GAMMA ( X ).
• BETA_CDF_VALUES returns some values of the Beta CDF.
• GAMMA_LOG_VALUES returns some values of the Log Gamma function.
• MDBETA evaluates the incomplete beta function.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the C++ source codes.