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Phil Steitz commented on MATH540:

I see now that there actually does appear to be an error in the javadoc. The implementation
really returns the largest x such that p(X <= x) <= p. In the discrete case, <=
matters and I think both inequalities in the javadoc should be changed.
In your example, if the probability distribution vanishes outside 0, 1, 2, 3 and puts .25
mass on each of these values, the inverse cumulative probability function evaluated at .0001
should be 1, as this is the largest value such that
p(X <= x) <= .0001.
If you fix your distribution so that both probability and cumulativeProbability return correct
values (rather than throwing NPEs) outside of the mass values, you should get 1 returned.
> AbstractIntegerDistribution.inverseCumulativeProbability(...) Bug
> 
>
> Key: MATH540
> URL: https://issues.apache.org/jira/browse/MATH540
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 2.1
> Reporter: Ole Ersoy
> Fix For: 3.0
>
> Attachments: DummyDiscreteDistribution.java, DummyDiscreteDistributionTest.java
>
>
> The AbstractIntegerDistribution.inverseCumulativeProbability(...) function attempts to
decrement the lower bound of discrete distributions to values that go below the lower bound.

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