asa310

asa310, a MATLAB code which computes the cumulative distribution function (CDF) of the noncentral Beta distribution, by Chattamvelli and Shanmugam.

This is a version of Applied Statistics Algorithm 310.

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

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 MIT license

Languages:

asa310 is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version

Related Data and Programs:

asa310_test

asa063, a MATLAB code which evaluates the incomplete Beta function.

asa109, a MATLAB code which inverts the incomplete Beta function.

asa226, a MATLAB code which computes the CDF of the noncentral Beta distribution.

beta_nc, a MATLAB code which evaluates the CDF of the noncentral Beta distribution.

prob, a MATLAB code which evaluates and inverts a number of probabilistic distributions.

test_values, a MATLAB code which contains sample values for a number of distributions.

toms179, a MATLAB code which evaluates the incomplete Beta function.

Author:

Original FORTRAN77 version by R Chattamvelli, R Shanmugam; Matlab version by John Burkardt.

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:

• alnorm.m computes the cumulative density of the standard normal distribution.
• 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.