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List:       jakarta-commons-dev
Subject:    [jira] [Commented] (MATH-692) Cumulative probability and inverse
From:       Sébastien_Brisard_(Commented)_(JIRA) <jira () apache ! org>
Date:       2011-12-31 17:12:30
Message-ID: 1596222127.55991.1325351550704.JavaMail.tomcat () hel ! zones ! apache ! org
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    [ https://issues.apache.org/jira/browse/MATH-692?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13178048#comment-13178048 \
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Sébastien Brisard commented on MATH-692:
----------------------------------------

{quote}
I see you already changed the seed in Well1024aTest.
{quote}

Yes I did, but is this really how we want {{Well2004aTest}} to pass?
                
> Cumulative probability and inverse cumulative probability inconsistencies
> -------------------------------------------------------------------------
> 
> Key: MATH-692
> URL: https://issues.apache.org/jira/browse/MATH-692
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 1.0, 1.1, 1.2, 1.3, 2.0, 2.1, 2.2, 2.2.1, 3.0
> Reporter: Christian Winter
> Priority: Minor
> Fix For: 3.0
> 
> Attachments: MATH-692_integerDomain_patch1.patch, Math-692_realDomain_patch1.patch
> 
> 
> There are some inconsistencies in the documentation and implementation of functions \
> regarding cumulative probabilities and inverse cumulative probabilities. More \
> precisely, '<' and '<=' are not used in a consistent way. Besides I would move the \
> function inverseCumulativeProbability(double) to the interface Distribution. A true \
> inverse of the distribution function does neither exist for Distribution nor for \
> ContinuosDistribution. Thus we need to define the inverse in terms of quantiles \
> anyway, and this can already be done for Distribution. On the whole I would declare \
> the (inverse) cumulative probability functions in the basic distribution interfaces \
> as follows: Distribution:
> - cumulativeProbability(double x): returns P(X <= x)
> - cumulativeProbability(double x0, double x1): returns P(x0 < X <= x1) [see also \
>                 1)]
> - inverseCumulativeProbability(double p):
> returns the quantile function inf{x in R | P(X<=x) >= p} [see also 2), 3), and 4)]
> 1) An aternative definition could be P(x0 <= X <= x1). But this requires to put the \
> function probability(double x) or another cumulative probability function into the \
> interface Distribution in order be able to calculate P(x0 <= X <= x1) in \
> AbstractDistribution. 2) This definition is stricter than the definition in \
> ContinuousDistribution, because the definition there does not specify what to do if \
> there are multiple x satisfying P(X<=x) = p. 3) A modification could be defined for \
> p=0: Returning sup{x in R | P(X<=x) = 0} would yield the infimum of the \
> distribution's support instead of a mandatory -infinity. 4) This affects issue \
>                 MATH-540. I'd prefere the definition from above for the following \
>                 reasons:
> - This definition simplifies inverse transform sampling (as mentioned in the other \
>                 issue).
> - It is the standard textbook definition for the quantile function.
> - For integer distributions it has the advantage that the result doesn't change \
> when switching to "x in Z", i.e. the result is independent of considering the \
> intergers as sole set or as part of the reals. ContinuousDistribution:
> nothing to be added regarding (inverse) cumulative probability functions
> IntegerDistribution:
> - cumulativeProbability(int x): returns P(X <= x)
> - cumulativeProbability(int x0, int x1): returns P(x0 < X <= x1) [see also 1) \
> above]

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