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https://issues.apache.org/jira/browse/MATH-699?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13146614#comment-13146614
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Christian Winter commented on MATH-699:
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Much discussion has happened here in the recent days. Thanks!
Now I realize that it is hard to get rid of the bracketing step in the case of
unbounded support. I guess a default bracket of
{{[-Double.MAX_VALUE;+Double.MAX_VALUE]}} for {{0<p<1}} isn't a good idea for
such cases. Maybe we can move the bracketing step into a {{getBracket(double
p)}} method (only {{0<p<1}} needs to be handled), which makes use of the
support bounds where possible and performs an bracketing algorithm only as last
option. For specific distributions this method can be overridden by providing
brackets through precomputed cdf-values or clever estimations, which removes
using an bracketing algorithm at all. Such a method allows to delete
{{getDomainLowerBound}}/{{getDomainUpperBound}}/{{getInitialDomain}}. However,
this replacement doesn't remove the pain caused by
{{getDomainLowerBound}}/{{getDomainUpperBound}}/{{getInitialDomain}}
completely. It is just a little mitigation to this pain as {{getBracket}}
doesn't have to be overridden (though it should be overridden to increase
performance unless {{inverseCumulativeProbability}} is overridden entirely).
For the plateau issue I unfortunately don't see a way to avoid implementing a
modified solver so that it approximates the solution by moving together {{x0}}
and {{x1}} satisfying {{P(X<=x0) < p}} and {{P(X<=x1) >= p}}.
> 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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