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From Sébastien Brisard (Commented) (JIRA) <j...@apache.org>
Subject [jira] [Commented] (MATH-699) inverseCumulativeDistribution fails with cumulative distribution having a plateau
Date Wed, 09 Nov 2011 06:55:51 GMT

    [ https://issues.apache.org/jira/browse/MATH-699?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13146814#comment-13146814
] 

Sébastien Brisard commented on MATH-699:
----------------------------------------

{quote}
A different idea for solving the bracketing issue: We could solve the inverse cdf calculation
by transforming the domain [-∞;+∞] to [-1;+1] with arctan. More precisely, we could do
the first iterations of the solving step on the transformed domain, and we can go back to
original domain as soon as +/-1 aren't interval limits any more.
{quote}

Is it not a "disguised" bracketting step, with a somewhat more clever way of sampling the
reals (as opposed to arithmetic progression)? In this case, maybe it would be just as simple
to perform a bracketting step, with *geometric* progression (as proposed by Christian), when
one of the bounds of the support is not finite.

{quote}
only 0<p<1 needs to be handled
{quote}
I guess you mean by that that what should be done is
* return {{getSupportLowerBound()}} when {{p == 0}},
* return {{getSupportUpperBound()}} when {{p == 1}}.

This means that the contract of {{getSupportLowerBound()}}/{{getSupportUpperBound()}} *requires*
that the returned values are actually the *best* bounds on the support. While I have no problem
with this sound requirement, I don't think this is currently stated clearly in the Javadoc,
but I'm no native english speaker...
                
> 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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