TOMS179 Modified Beta Function

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

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".

The text of many ACM TOMS algorithms is available online through ACM: http://calgo.acm.org/ or NETLIB: http://www.netlib.org/toms/index.html.

Usage:

prob = mdbeta ( x, p, q, &ier )
where
• 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 FORTRAN90 version and a MATLAB version and a Python 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.

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.

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:

Last revised on 19 August 2019.