[
https://issues.apache.org/jira/browse/MATH-692?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
]
Christian Winter updated MATH-692:
----------------------------------
Attachment: Math-692_realDomain_patch1.patch
Here is the first patch for this issue (unfortunately with some delay). It
adjusts the distributions with real domain to the definitions in this issue,
and it mainly changes documentations.
I could not move inverseCumulativeProbability(double) up to Distribution
because there would be a conflict with
IntegerDistribution.inverseCumulativeProbability(double): This method returns
int. This problem will be removed by solving issue MATH-703.
The implementation of inverseCumulativeProbability(double) is not changed as
Sébastien is working on this.
I will provide the patch for the integer distributions as soon as I have
adjusted the test data to the new inequalities and reverified the adjusted test
data.
> 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_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]
--
This message is automatically generated by JIRA.
If you think it was sent incorrectly, please contact your JIRA administrators:
https://issues.apache.org/jira/secure/ContactAdministrators!default.jspa
For more information on JIRA, see: http://www.atlassian.com/software/jira
