ASA310
CDF of the noncentral Beta distribution

ASA310 is a MATLAB 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.

Related Data and Programs:

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

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

ASA226 is a MATLAB library which computes the CDF of the noncentral Beta distribution.

ASA310 is also available in a C++ version and a FORTRAN77 version and a FORTRAN90 version

BETA_NC is a MATLAB 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 MATLAB library which evaluates and inverts a number of probabilistic distributions.

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

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

TOMS708 is 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:

• alngam.m computes the logarithm of the gamma function.
• alnorm.m computes the cumulative density of the standard normal distribution.
• beta_noncentral_cdf.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.
• gammad.m computes the Incomplete Gamma Integral
• ncbeta.m computes the noncentral Beta CDF.
• timestamp.m prints out the current YMDHMS date as a timestamp.

Examples and Tests:

• asa310_test.m, a sample calling program.
• asa310_test01.m, tests NCBETA.
• asa310_test_output.txt, the output file.

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