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Sébastien Brisard commented on MATH738:

In {{r1415853}}, committed new implementation of {{Beta.logBeta(double, double)}}. The accuracy
of the new implementation is reported in the table below. This change of the code leads to
the deprecation of {{Beta.logBeta(double, double, double, int)}}, as the computation is no
longer iterative.
 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  1.80 ulps  81.08 ulps  14031.0 ulps 
 0 < x ≤ 8, 8 < y ≤ 16  x[i] = i / 32, i = 1, ..., 256, y[j] = j / 32, j
= 257, ..., 512  0.50 ulps  3.64 ulps  694.0 ulps 
 0 < x ≤ 8, 16 < y ≤ 256  x[i] = i / 32, i = 1, ..., 256, y[j] = j, j = 17,
..., 256  1.04 ulps  139.32 ulps  34509.0 ulps 
 8 < x ≤ 16, 8 < y ≤ 16  x[i] = i / 32, i = 257, ..., 512, y[j] = j / 32,
j = 257, ..., 512  0.35 ulps  0.48 ulps  2.0 ulps 
 8 < x ≤ 16, 16 < y ≤ 256  x[i] = i / 32, i = 257, ..., 512, y[j] = j, j = 17,
..., 256  0.31 ulps  0.47 ulps  2.0 ulps 
 16 < x ≤ 256, 16 < y ≤ 256  x[i] = i, i = 17, ..., 256, y[j] = j, j = 17, ...,
256  0.35 ulps  0.49 ulps  2.0 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: 3.2, 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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