toms179

toms179, a MATLAB code which implements ACM TOMS algorithm 179, for evaluating the modified Beta function.

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

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.

Licensing:

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

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:

toms179_test

asa063, a MATLAB code which evaluates the incomplete beta function.

asa109, a MATLAB code which inverts the incomplete beta function.

asa226, a MATLAB code which evaluates the cdf of the noncentral beta distribution.

asa310, a MATLAB code which computes the cdf of the noncentral beta distribution.

beta_nc, a MATLAB code 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 code which contains routines which evaluate a number of probability density functions, including one based on the beta function.

test_values, a MATLAB code 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:

• 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.