[jira] [Commented] (MATH-1257) NormalDistribution.cumulativeProbability() suffers from cancellation

["Gilles (JIRA)" <ji...@apache.org>]

    [ https://issues.apache.org/jira/browse/MATH-1257?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=14702901#comment-14702901 ] 

Gilles commented on MATH-1257:
------------------------------

bq. return 0.5 * Erf.erfc( -dev / standardDeviation * SQRT2 );

Using either the current code or
{code}
return 0.5 * Erf.erfc(-dev / (standardDeviation * SQRT2));
{code}
the unit tests pass.

bq. \[...\] test cases for "extreme values" \[...\]

A patch with a test case that shows the problem would be welcome.



> 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
>
> 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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