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https://issues.apache.org/jira/browse/STATISTICS-37?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Alex Herbert resolved STATISTICS-37.
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Fix Version/s: 1.0
Resolution: Implemented
> Better inverse Erfc function for the Normal distribution
> --------------------------------------------------------
>
> Key: STATISTICS-37
> URL: https://issues.apache.org/jira/browse/STATISTICS-37
> Project: Apache Commons Statistics
> Issue Type: Improvement
> Components: distribution
> Affects Versions: 1.0
> Reporter: Alex Herbert
> Priority: Major
> Fix For: 1.0
>
>
> The Normal distribution uses InverseErfc for the inverse CDF. This is a
> wrapper for InverseErf and as such it is limited in precision as p -> 0 since
> the method computes using (2p - 1). When p is < 1e-16 then the inverse CDF
> returns -infinity. The smallest z is around -8.2
> as computed by matlab:
> norminv(1e-16)
> -8.222082216130437
> scipy, R, matlab, octave, Mathematica all have methods to invert small p.
> Here is output from matlab for norminv(5e-324): -38.472346342768788. It is
> accurate down to the minimum value for a 64-bit float.
> There are two free libraries that seem to be used for this: Boost and Cephes
> (function ntdri). The Boost licence is compatible with Apache and there are
> some Boost derived works already in Commons Numbers. Incorporating the Boost
> Erf functions into numbers would be useful.
> The inability to invert the Erfc for all p affects the Normal, Truncated
> normal and Levy distributions.
> Boost error function inverses:
> [https://www.boost.org/doc/libs/1_77_0/libs/math/doc/html/math_toolkit/sf_erf/error_inv.html]
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