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From "Christian Winter (Commented) (JIRA)" <>
Subject [jira] [Commented] (MATH-699) inverseCumulativeDistribution fails with cumulative distribution having a plateau
Date Tue, 08 Nov 2011 22:39:51 GMT


Christian Winter commented on MATH-699:

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:
>             Project: Commons Math
>          Issue Type: Bug
>    Affects Versions: 3.0
>            Reporter: S├ębastien Brisard
>            Assignee: S├ębastien Brisard
>            Priority: Minor
>         Attachments:
> 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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