jburkardt

TOMS179\ Modified Beta Function {#toms179-modified-beta-function align=”center”} ======================

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TOMS179 is a C++ 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.md, 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: {#usage align=”center”}

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.

Licensing: {#licensing align=”center”}

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

Languages: {#languages align=”center”}

TOMS179 is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs: {#related-data-and-programs align=”center”}

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.

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

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.

TOMS708, a FORTRAN90 library which evaluates the incomplete beta function.

Reference: {#reference align=”center”}

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: {#source-code align=”center”}

• toms179.cpp, the source code.
• toms179.hpp, the include file.

Examples and Tests: {#examples-and-tests align=”center”}

• toms179_prb.cpp, a sample calling program.
• toms179_prb_output.txt, the output from a run of the sample program.

List of Routines: {#list-of-routines align=”center”}

• ALOGAM calculates the natural logarithm of GAMMA ( X ).
• BETA_CDF_VALUES returns some values of the Beta CDF.
• GAMMA_LOG_VALUES returns some values of the Log Gamma function.
• MDBETA evaluates the incomplete beta function.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the C++ source codes.

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Last revised on 30 January 2008.