TOMS179
Modified Beta Function

TOMS179 is a MATLAB program, using double precision arithmetic, 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 )

where X is the point of evaluation, p and q are parameters, prob is the computed probability, and ier is an error flag.

Related Data and Programs:

ASA063 is a MATLAB library which evaluates the incomplete Beta function.

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

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

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

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

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

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

TEST_VALUES is 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 is 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.