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https://issues.apache.org/jira/browse/MATH-437?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12975771#action_12975771
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Mikkel Meyer Andersen commented on MATH-437:
--------------------------------------------
In the past months, I've communicated with both Richard Simard and George
Marsaglia regarding small disagreement between theory in Marsaglia's article
and the actual implementation; namely the fact that 0 <= h < 1, but in the code
0 < h <= 1. I wrote to Marsaglia regarding this, and his answer was:
{quote}
The Kolmogorov distribution comes from a piecewise polynomial in h with knots
at 1/2n, 2/2n,...,(2n-1)/2n, with each segment assumed to start with h=0.
Although I emphasized that 0<= h <1 in the article, I overlooked the need for
ensuring that in the C code, and apparently so did my colleagues. Sorry about
that.
{quote}
This means that his code has to be changed slightly to ensure that 0 <= h < 1.
Simard argues that this shouldn't mean anything because KS distribution is
continuous, but if one wants to correct it, one should
{quote}
Instead of taking the floor(n*d + 1) and making this correction for h = 1, take
the ceiling (n*d).
{quote}
I would prefer using ceiling (n*d) instead of the originally (wrongly) proposed
floor(n*d + 1), despite arguments of continuity. So my plan is to do this (I
still have my implementation which seem to work quite okay). The only problem
is that R seems to use Marsaglia's code, and I don't have access to e.g.
Mathematica which should implement several algorithms, so I might run into
problems when I have to perform tests.
> 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
> Fix For: 3.0
>
> 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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