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https://issues.apache.org/jira/browse/MATH-699?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13146108#comment-13146108
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Sébastien Brisard commented on MATH-699:
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I agree with you: however careful we are, the default implementation will never
be perfect, and it should be clearly stated in the javadoc. I see (but haven't
dug into it yet) there is an abstract test for continuous distributions. I'll
try and make sure that most possible cases of failure of
{{inverseCumulativeProbability}} are tested in this abstract framework, so that
users could be *strongly* encouraged to implement this test for their very
specific distribution.
I do think we can widen a little bit the scope of the default implementation. I
actually worked towards eliminating the bracketing step, but you convinced me
that it should be the other way round: can we eliminate the
domainLower/upperBound methods (which I agree are very efficient, but a little
bit of a pain in the neck...).
Here is an idea I'm going to check (keeping in mind the accuracy issues you've
already pointed at)
* for distributions with bounded support: maybe the bounds (possibly shifted if
the bounds are not inclusive) of the support itself could be used as an initial
bracketting range.
* for distributions with unbounded support: start from *any* (? or a better
guess? average value?) point in the support, and do bracketting. However, I do
agree with Christian, we should use geometric progressions in this case,
instead of arithmetic progressions. This would probably lead to a very large
interval, but it would provide us an interval more quickly, and the solver
itself would probably be quite good at narrowing it very quickly. I can try
some monitoring on this issue.
As for plateaus, I think what I'm currently working on is not too inefficient.
I'm sure it's not *the* answer (which is, anyway, 42 :)), but I'm struggling to
fail this algo... Don't worry, I'll break it. I think that what I've done
entails very little additional cost (maybe one more evaluation of
cumulativeProbability) for distributions *without* plateau, but I need to check
that (we do not want to pay a heavy price for plateaus, since most of our
distributions do not have one, as you rightly pointed out).
I would be grateful for any idea on these topics, and will keep you informed.
All the best for now,
Sébastien
> inverseCumulativeDistribution fails with cumulative distribution having a
> plateau
> ---------------------------------------------------------------------------------
>
> Key: MATH-699
> URL: https://issues.apache.org/jira/browse/MATH-699
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 3.0
> Reporter: Sébastien Brisard
> Assignee: Sébastien Brisard
> Priority: Minor
> Attachments: AbstractContinuousDistributionTest.java
>
>
> This bug report follows MATH-692. The attached unit test fails. As required
> by the definition in MATH-692, the lower-bound of the interval on which the
> cdf is constant should be returned. This is not so at the moment.
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