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From Sébastien Brisard (JIRA) <j...@apache.org>
Subject [jira] [Commented] (MATH-738) Incomplete beta function I(x, a, b) is inaccurate for large values of a and/or b
Date Wed, 13 Mar 2013 06:22:13 GMT

    [ https://issues.apache.org/jira/browse/MATH-738?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13600880#comment-13600880
] 

Sébastien Brisard commented on MATH-738:
----------------------------------------

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: MATH-738
>                 URL: https://issues.apache.org/jira/browse/MATH-738
>             Project: Commons Math
>          Issue Type: Bug
>    Affects Versions: 3.0
>            Reporter: Sébastien Brisard
>              Labels: special-functions
>             Fix For: 3.2, 4.0
>
>
> This was first reported in MATH-718. The result of the current implementation of the
incomplete beta function I(x, a, b) is inaccurate when a and/or b are large-ish. 
> I've skimmed through [slatec|http://www.netlib.org/slatec/fnlib/betai.f], GSL, [Boost|http://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
[TOMS-708|http://www.netlib.org/toms/708] is probably the best option.

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