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https://issues.apache.org/jira/browse/MATH-785?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13279874#comment-13279874
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Thomas Neidhart commented on MATH-785:
--------------------------------------
I looked further into it and am not convinced anymore that this really to solve
the numerical stability problems. In fact the results are pretty much random
depending on the choice of the scaling factor.
In fact I implemented the modified Lentz-Thompson algorithm to do the continued
fraction evaluation and the results are much much better. All the unit tests
run through and the probability evaluations for the different distributions for
large trials are stable and return correct values.
> Numerical Underflow in ContinuedFraction
> ----------------------------------------
>
> Key: MATH-785
> URL: https://issues.apache.org/jira/browse/MATH-785
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 3.0
> Environment: Issue seen in both 3.0 release binary version as well as
> a fresh checkout of the subversion trunk.
> java -version output:
> java version "1.6.0_26"
> Java(TM) SE Runtime Environment (build 1.6.0_26-b03)
> Java HotSpot(TM) 64-Bit Server VM (build 20.1-b02, mixed mode)
> (On Ubuntu 12.04)
> Reporter: Colin J. Fuller
> Attachments: patch.txt
>
>
> The ContinuedFraction calculation can underflow in the evaluate method,
> similar to the overflow case already dealt with. I encountered this problem
> while trying to evaluate the inverse cumulative probability of an F
> distribution with a large number of degrees of freedom.
> I would guess this has the same cause as MATH-718 and MATH-738, though I am
> not experiencing inaccurate results but rather an exception.
> For instance, the following test case fails:
> double prob = 0.01;
> FDistribution f = new FDistribution(200000, 200000);
> double fails = f.inverseCumulativeProbability(prob);
> This produces a NoBracketingException with the following stack trace:
> org.apache.commons.math3.exception.NoBracketingException: function values at
> endpoints do not have different signs, endpoints: [0, 1], values: [-0.01, -∞]
> at
> org.apache.commons.math3.analysis.solvers.BrentSolver.doSolve(BrentSolver.java:118)
> at
> org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver.solve(BaseAbstractUnivariateSolver.java:190)
> at
> org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver.solve(BaseAbstractUnivariateSolver.java:195)
> at
> org.apache.commons.math3.analysis.solvers.UnivariateSolverUtils.solve(UnivariateSolverUtils.java:77)
> at
> org.apache.commons.math3.distribution.AbstractRealDistribution.inverseCumulativeProbability(AbstractRealDistribution.java:156)
> I could avoid the issue as in the comment to MATH-718 by relaxing the default
> value of epsilon in ContinuedFraction, although in my test case I can't see
> any reason the current default precision shouldn't be attainable.
> I fixed the issue by implementing underflow detection in ContinuedFraction
> and rescaling to larger values similarly to how the overflow detection that
> is already there works. I will attach a patch shortly.
> One possible issue with this fix is that if there exists a case where there
> is a legitimate reason for p2 or q2 to be zero (I cannot think of one), it
> might break that case.
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