ASA226
CDF of the noncentral Beta Distribution

ASA226 is a FORTRAN77 program, using double precision arithmetic, which evaluates the cumulative distribution function (CDF) of the noncentral Beta Distribution.

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.

Related Data and Programs:

ASA063 is a FORTRAN77 library which evaluates the incomplete Beta function.

ASA109 is a FORTRAN77 library which inverts the incomplete Beta function.

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

ASA310 is a FORTRAN77 library which computes the CDF of the noncentral Beta distribution.

BETA_NC is a FORTRAN90 library which evaluates the CDF of the noncentral Beta distribution.

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

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

PROB is a FORTRAN90 library which evaluates and inverts a number of probabilistic distributions.

TEST_VALUES is a FORTRAN77 library which contains sample values for a number of distributions.

TOMS179 is a FORTRAN77 library which evaluates the incomplete Beta function.

TOMS708 is a FORTRAN77 library which evaluates the incomplete Beta function.

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:

• asa226.f, the source code.
• asa226.csh, commands to compile the source code.

Examples and Tests:

• asa226_prb.f, a sample calling program.
• asa226_prb.csh, commands to compile and run the sample program.
• asa226_prb_output.txt, the output file.

List of Routines:

• ALNGAM computes the logarithm of the Gamma function.
• BETA_NONCENTRAL_CDF_VALUES returns some values of the noncentral Beta CDF.
• BETAIN computes the incomplete Beta function ratio.
• BETANC computes the tail of the noncentral Beta distribution.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the FORTRAN77 source codes.