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https://issues.apache.org/jira/browse/MATH-981?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13667631#comment-13667631
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Thomas Neidhart commented on MATH-981:
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It is not actually more accurate than the existing implementation, at least I
am not sure as I just compared the existing one with the new one. I have no
idea yet how accurate the existing implementation is.
The algorithm itself comes with a so-called refinement procedure to reduce the
error:
||Method||Error vs. Current||Speed vs. Current||
|New|< 1e-8|~ factor 10 faster|
|New + Refinement|< 1e-10|slightly slower|
Now there are some use-cases where the accuracy of this algorithm is sufficient
and the speed improvement would be quite interesting. One example is the
RandomGenerator#nextGaussian() method. Right now, the BitsStreamGenerator
(which is the base class for many of the fast ones like Well and
MersenneTwister), does use a clever technique involving trigonometry functions
to do the transformation from [0, 1] to a normally distributed value. This is
much faster than calling inverseCumulativeProbability() on a normal
distribution. The proposed algorithm is even faster than this method, so we
could consider using it for this purpose.
We could also add this algorithm as FastMath#getInverseCDF(boolean
errorCorrection) in case somebody wants to use a fast but less accurate variant
of this.
This is especially interesting for Monte Carlo simulations imho.
> An improved algorithm for computing the inverse cumulative probability for
> the normal distribution
> --------------------------------------------------------------------------------------------------
>
> Key: MATH-981
> URL: https://issues.apache.org/jira/browse/MATH-981
> Project: Commons Math
> Issue Type: Sub-task
> Reporter: Thomas Neidhart
> Priority: Minor
>
> The following page outlines an algorithm (and alternative algorithms) to
> compute the inverse cumulative probability for the normal distribution:
> http://home.online.no/~pjacklam/notes/invnorm/
> An implementation of this is also included in the referred contribution for a
> Monte Carlo engine.
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