TOMS179
Modified Beta Function
TOMS179
is a Python 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 )
where

x is the point of evaluation;

p and q are parameters;

prob, (output), is the computed probability;
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:
TEST_VALUES,
a Python library which
contains routines which return sample values of various functions,
including the modified beta function, and the logarithm of the
gamma function.
Reference:

Nancy Bosten, EL Battiste,
Remark on Algorithm 179:
Incomplete Beta Ratio,
Communications of the ACM,
Volume 17, Number 3, March 1974, pages 156157.

William Cody, Kenneth Hillstrom,
Chebyshev Approximations for the Natural Logarithm of the
Gamma Function,
Mathematics of Computation,
Volume 21, Number 98, April 1967, pages 198203.

John Hart, Ward Cheney, Charles Lawson, Hans Maehly,
Charles Mesztenyi, John Rice, Henry Thacher,
Christoph Witzgall,
Computer Approximations,
Wiley, 1968,
LC: QA297.C64.

Oliver Ludwig,
Algorithm 179:
Incomplete Beta Ratio,
Communications of the ACM,
Volume 6, Number 6, June 1963, page 314.

Malcolm Pike, Jennie SooHoo,
Remark on Algorithm 179:
Incomplete Beta Ratio,
ACM Transactions on Mathematical Software,
Volume 2, Number 2, June 1976, pages 207208.
Source Code:
You can go up one level to
the Python source codes.
Last revised on 18 August 2015.