ASA226
CDF of the noncentral Beta Distribution

ASA226 is a MATLAB library which evaluates the cumulative distribution function (CDF) of the noncentral Beta Distribution, by Russell Lenth.

ASA226 is Applied Statistics Algorithm 226. Source code for many Applied Statistics Algorithms is available through STATLIB.

The program can produce reasonably accurate answers for values of the noncentrality parameter up to about 100.

Note that an improvement to ASA226 was suggested by Frick, and implemented in the online copy available through STATLIB. When I run the improved copy, the computation fails. Therefore, the version I have put together has suppressed the improvement for now until I can determine the stray minus sign or logic error causing the problem.

Licensing:

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

Languages:

ASA226 is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version

Related Data and Programs:

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

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

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

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

DCDFLIB, a FORTRAN90 library which evaluates and inverts a number of statistical distributions.

GSL, a C++ library which includes many routines for evaluating probability distributions.

PROB, a MATLAB library which evaluates and inverts a number of probabilistic distributions.

TEST_VALUES, a MATLAB library which contains sample values for a number of distributions.

TOMS179, a MATLAB library which evaluates the incomplete Beta function.

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

Author:

Original FORTRAN77 version by Russell Lenth; Matlab version by John Burkardt.

Reference:

1. H Frick,
   Algorithm AS R84: A Remark on Algorithm AS 226: Computing Noncentral Beta Probabilities,
   Applied Statistics,
   Volume 39, Number 2, 1990, pages 311-312.
2. Russell Lenth,
   Algorithm AS 226: Computing Noncentral Beta Probabilities,
   Applied Statistics,
   Volume 36, Number 2, 1987, pages 241-244.

Source Code:

• alngam.m computes the logarithm of the Gamma function.
• beta_noncentral_cdf_values.m returns some values of the noncentral Beta CDF.
• betain.m computes the incomplete Beta function ratio.
• betanc.m computes the tail of the noncentral Beta distribution.
• timestamp.m prints out the current YMDHMS date as a timestamp.

Examples and Tests:

• asa226_test.m, a sample calling program.
• asa226_test01.m, tests BETANC.
• asa226_test_output.txt, the output file.

You can go up one level to the MATLAB source codes.