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https://issues.apache.org/jira/browse/MATH-1257?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=14703489#comment-14703489
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Otmar Ertl commented on MATH-1257:
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+1 for the patch, it eliminates one source of error. For values much smaller
than -1 the regularizedGammaQ function evaluates to a very small positive
values. The computation was like 0.5*((regularizedGammaQ - 1) + 1). With the
patch the computation is now 0.5*regularizedGammaQ, obviously improving
accuracy.
> NormalDistribution.cumulativeProbability() suffers from cancellation
> --------------------------------------------------------------------
>
> Key: MATH-1257
> URL: https://issues.apache.org/jira/browse/MATH-1257
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 3.5
> Reporter: Bill Murphy
> Priority: Minor
> Attachments: MATH-1257.patch
>
>
> I see the following around line 194:
> {noformat}
> return 0.5 * (1 + Erf.erf(dev / (standardDeviation * SQRT2)));
> {noformat}
> When erf() returns a very small value, this cancels in the addition with the
> "1.0" which leads to poor precision in the results.
> I would suggest changing this line to read more like:
> {noformat}
> return 0.5 * Erf.erfc( -dev / standardDeviation * SQRT2 );
> {noformat}
> Should you want some test cases for "extreme values" (one might argue that
> within 10 standard deviations isn't all that extreme) then you can check the
> following: http://www.jstatsoft.org/v52/i07/ then look in the v52i07-xls.zip
> at replication-01-distribution-standard-normal.xls
> I think you will also find that evaluation of expressions such as
> {noformat}NormalDistribution( 0, 1 ).cumulativeProbability( -10.0 );{noformat}
> are pretty far off.
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