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From Mikkel Meyer Andersen <m...@mikl.dk>
Subject [MATH] Fwd: [jira] Commented: (MATH-437) Kolmogorov Smirnov Distribution
Date Tue, 16 Nov 2010 07:37:37 GMT
Dear developers,

We now have a working implementation of the cdf for the two-sided
Kolmogorov Smirnov Distribution [1]. What do you think about it? Now
both rounding (RealMatrix and its cousins) and exact (using
BigFraction and its cousins) are provided - the exact should only be
used for verification purposes because its way too slow in practise.
Should the exact be removed or should be JavaDoc just reflect this
fact clearly? I like it being there - it also gives the user to
possibility to use it for e.g. n <= 50. On the negative side, two
pow-functions are required (no common superclass for FieldMatrix<T>
and RealMatrix providing multiply-functionality - unfortunately).

Cheers, Mikkel.

[1]: https://issues.apache.org/jira/browse/MATH-437

---------- Forwarded message ----------
From: Mikkel Meyer Andersen (JIRA) <jira@apache.org>
Date: 2010/11/16
Subject: [jira] Commented: (MATH-437) Kolmogorov Smirnov Distribution
To: mikl@mikl.dk



   [ https://issues.apache.org/jira/browse/MATH-437?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12932361#action_12932361
]

Mikkel Meyer Andersen commented on MATH-437:
--------------------------------------------

The last part of the roundedK kan be replaced with
{{
double pFrac = Hpower.getEntry(k - 2, k - 2);

for (int i = 1; i <= n; ++i) {
       pFrac *= (double)i / (double)n;
}

return pFrac;
}}
to get even better running time and still precise results:
{{
F(n, x) = F(200, 0.02):
                                Lecuyer (3.0 ms.) = 5.151982014280042E-6
  KolmogorovSmirnovDistribution exact (760.0 ms.) = 5.15198201428005E-6
  KolmogorovSmirnovDistribution !exact (16.0 ms.) = 5.151982014280049E-6
-------------------------


F(n, x) = F(200, 0.031111):
                                Lecuyer (2.0 ms.) = 0.012916146481628863
 KolmogorovSmirnovDistribution exact (51902.0 ms.) = 0.012149763742041911
   KolmogorovSmirnovDistribution !exact (9.0 ms.) = 0.012149763742041922
-------------------------


F(n, x) = F(200, 0.04):
                                Lecuyer (0.0 ms.) = 0.1067121882956352
 KolmogorovSmirnovDistribution exact (5903.0 ms.) = 0.10671370113626812
   KolmogorovSmirnovDistribution !exact (6.0 ms.) = 0.10671370113626813
-------------------------
}}

> Kolmogorov Smirnov Distribution
> -------------------------------
>
>                 Key: MATH-437
>                 URL: https://issues.apache.org/jira/browse/MATH-437
>             Project: Commons Math
>          Issue Type: New Feature
>            Reporter: Mikkel Meyer Andersen
>            Assignee: Mikkel Meyer Andersen
>            Priority: Minor
>         Attachments: KolmogorovSmirnovDistribution.java
>
>   Original Estimate: 0.25h
>  Remaining Estimate: 0.25h
>
> Kolmogorov-Smirnov test (see [1]) is used to test if one sample against a known probability
density functions or if two samples are from the same distribution. To evaluate the test statistic,
the Kolmogorov-Smirnov distribution is used. Quite good asymptotics exist for the one-sided
test, but it's more difficult for the two-sided test.
> [1]: http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test

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