ASA310
CDF of the noncentral Beta distribution

ASA310 is a C++ library which computes the cumulative distribution function (CDF) of the noncentral Beta distribution.

ASA310 is Applied Statistics Algorithm 310. Source code for many Applied Statistics Algorithms is available through STATLIB.

Warning: I could not get this algorithm to perform properly until I had made a number of corrections.

Note that the printed text of the algorithm, and the online version distributed by APSTAT, omit a crucial initialization of the variable S to zero.

Moreover, there are two typographical errors introduced into the online version distributed by APSTAT; in both cases a multiplication symbol became a minus sign.

Finally, note that the authors of AS 310 invoke AS 226, but specifically recommend that the changes submitted by Frick NOT be included. The version of AS 226 distributed by APSTAT includes the Frick changes; the version of AS310 distributed by APSTAT includes this copy of AS 226, and hence the changes suggested by Frick.

Licensing:

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

Languages:

ASA310 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 C++ library which evaluates the incomplete Beta function.

ASA109, a C++ library which inverts the incomplete Beta function.

ASA226, 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 evaluates and inverts a number of statistical distributions.

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

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

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

TOMS179, a C++ library which evaluates the incomplete Beta function.

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

Reference:

1. R Chattamvelli, R Shanmugam,
   Algorithm AS 310: Computing the Non-central Beta Distribution Function,
   Applied Statistics,
   Volume 46, Number 1, 1997, pages 146-156.
2. 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.
3. Russell Lenth,
   Algorithm AS 226: Computing Noncentral Beta Probabilities,
   Applied Statistics,
   Volume 36, Number 2, 1987, pages 241-244.

Source Code:

• asa310.cpp, the source code.
• asa310.hpp, the include file.
• asa310.sh, commands to compile the source code.

Examples and Tests:

• asa310_prb.cpp, a sample calling program.
• asa310_prb.sh, commands to compile and run the sample program.
• asa310_prb_output.txt, the output file.

List of Routines:

• ALNORM computes the cumulative density of the standard normal distribution.
• 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.
• GAMMAD computes the Incomplete Gamma Integral
• NCBETA computes the noncentral Beta CDF.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

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