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Sébastien Brisard commented on MATH738:

I don't think these improvements are sufficient (the issue is really with the incomplete beta
function, while I started with the beta function). The accuracy of the incomplete beta function
should first be assessed (for example with the tools I have provided). In any case, this issue
cannot be solved until 4.0, since there is a deprecated funtion which cannot be removed before
4.0.
Improving the incomplete beta function is a lot of work. I have provided the references in
the javadoc (mainly the NSWC FORTRAN library). As I have already indicated, I no longer have
time to do it myself (I'm sorry I forgot to remove myself as an assignee for this ticket).
If someone is willing to take over, I'm happy to provide some help and references, but I just
can't find the time to do the job. Hope you will understand.
> Incomplete beta function I(x, a, b) is inaccurate for large values of a and/or b
> 
>
> Key: MATH738
> URL: https://issues.apache.org/jira/browse/MATH738
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 3.0
> Reporter: Sébastien Brisard
> Labels: specialfunctions
> Fix For: 3.2, 4.0
>
>
> This was first reported in MATH718. The result of the current implementation of the
incomplete beta function I(x, a, b) is inaccurate when a and/or b are largeish.
> I've skimmed through [slatechttp://www.netlib.org/slatec/fnlib/betai.f], GSL, [Boosthttp://www.boost.org/doc/libs/1_38_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html]
as well as NR. At first sight, neither uses the same method to compute this function. I think
[TOMS708http://www.netlib.org/toms/708] is probably the best option.

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