[ https://issues.apache.org/jira/browse/MATH-738?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13500067#comment-13500067 ]
Sébastien Brisard commented on MATH-738:
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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: MATH-738
> URL: https://issues.apache.org/jira/browse/MATH-738
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 3.0
> Reporter: Sébastien Brisard
> Assignee: Sébastien Brisard
> Labels: special-functions
> Fix For: 3.1, 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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