[ https://issues.apache.org/jira/browse/MATH738?page=com.atlassian.jira.plugin.system.issuetabpanels:commenttabpanel&focusedCommentId=13500067#comment13500067
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Sébastien Brisard commented on MATH738:

Starting first with {{Beta.logBeta(double, double)}}, accuracy of the current {{r}} implementation
as reported in the users guide is
 Interval  Values tested
 Average error  Standard deviation  Maximum error 
 0 < x ≤ 8, 0 < y ≤ 8  {{x[i] = i / 32, i = 1, ..., 256}}, {{y[j] = j /
32, j = 1, ..., 256}}  5.04 ulps  270.99 ulps  46696.0 ulps 
 0 < x ≤ 8, 8 < y ≤ 16  {{x[i] = i / 32, i = 1, ..., 256}}, {{y[j] = j /
32, j = 257, ..., 512}}  9.75 ulps  149.42 ulps  19126.0 ulps 
 0 < x ≤ 8, 16 < y ≤ 256  {{x[i] = i / 32, i = 1, ..., 256}}, {{y[j] = j, j
= 17, ..., 256}}  357.82 ulps  39297.58 ulps  8635522.0 ulps 
 8 < x ≤ 16, 8 < y ≤ 16  {{x[i] = i / 32, i = 257, ..., 512}}, {{y[j] = j
/ 32, j = 257, ..., 512}}  2.37 ulps  13.0 ulps  1.9 ulps 
 8 < x ≤ 16, 16 < y ≤ 256  {{x[i] = i / 32, i = 257, ..., 512}}, {{y[j] = j,
j = 17, ..., 256}}  10.75 ulps  9.74 ulps  73.0 ulps 
 16 < x ≤ 256, 16 < y ≤ 256  {{x[i] = i, i = 17, ..., 256}}, {{y[j] = j, j = 17,
..., 256}}  5.20 ulps  4.33 ulps  53.0 ulps 
> 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
> Assignee: Sébastien Brisard
> Labels: specialfunctions
> Fix For: 3.1, 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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