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https://issues.apache.org/jira/browse/MATH-718?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13253381#comment-13253381
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Thomas Neidhart commented on MATH-718:
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The problem is not only related to the Beta function, also the
ContinuedFraction.evaluate is numerically unstable.
The reason the cumulativeProbability returns infinity instead of NaN is because
the evaluate return 0.0 when called from Beta.regularizedBeta, which leads to a
division by zero. The used default epsilon of 10e-15 seems also quite
restrictive, when relaxing the epsilon I got much better results (e.g. with
10e-5 I got a result of 499997).
> inverseCumulativeProbability of BinomialDistribution returns wrong value for
> large trials.
> ------------------------------------------------------------------------------------------
>
> Key: MATH-718
> URL: https://issues.apache.org/jira/browse/MATH-718
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 2.2, 3.0
> Reporter: Yuji Uchiyama
> Assignee: Sébastien Brisard
> Fix For: 3.1, 4.0
>
>
> The inverseCumulativeProbability method of the BinomialDistributionImpl class
> returns wrong value for large trials. Following code will be reproduce the
> problem.
> {{System.out.println(new BinomialDistributionImpl(1000000,
> 0.5).inverseCumulativeProbability(0.5));}}
> This returns 499525, though it should be 499999.
> I'm not sure how it should be fixed, but the cause is that the
> cumulativeProbability method returns Infinity, not NaN. As the result the
> checkedCumulativeProbability method doesn't work as expected.
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