TOMS179
Modified Beta Function

TOMS179 is a MATLAB 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, ier ] = mdbeta ( x, p, q )

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

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 MATLAB library which evaluates the incomplete Beta function.

ASA109, a MATLAB library which inverts the incomplete Beta function.

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

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

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

DCDFLIB, a FORTRAN90 library which contains routines which evaluate a number of probability density functions, including one based on the Beta function.

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

TEST_VALUES, 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.

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:

• alogam.m calculates the natural logarithm of GAMMA ( X ).
• beta_cdf_values.m returns some values of the Beta CDF.
• gamma_log_values.m returns some values of the Log Gamma function.
• mdbeta.m evaluates the incomplete beta function.
• timestamp.m TIMESTAMP prints out the current YMDHMS date as a timestamp.

Examples and Tests:

• toms179_test.m, a sample calling program.
• toms179_test01.m, tests ALOGAM.
• toms179_test02.m, tests MDBETA.
• toms179_test_output.txt, the output from a run of the sample program.

You can go up one level to the MATLAB source codes.