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Topic: Kolmogorov–Smirnov / Lilliefors test, small sample
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Replies: 5   Last Post: Aug 11, 2013 5:23 PM

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David Jones

Posts: 62
Registered: 2/9/12
Re: Kolmogorov–Smirnov / Lillief
ors test, small samples

Posted: Jul 24, 2013 2:42 PM
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wrote in message
news:c839757f-37aa-4d47-9e4f-feb19f3abd24@googlegroups.com...

Thanks, Dave. I think I requested the Biometrika and I'll look into the 2nd
one when I get back to home base next week.

Yes, I see why checking delta F(x) and delta F(x-) at each sample datum x
solves the problem. I wonder though whether the Lilliefors thresholds (for
example, in their paper) were generated with the statistic defined in this
way. Or is it the case that nowadays there are a plethora of threshold
tables, each with their own particular definition, ideally documented to
this level of detail.

===========================================================================

I think the treatment of the KS statistic was well-established well before
Lilliefors in 1967.

Modern treatments tend to present results for the critical points in a
different way,.... via an adjustment formula using the sample size to give
an adjusted statistic to refer to a simple table (one value for each
percentage point). Results have been published for several types for
distribution being fitted, including "no-fitting". The last case would
enable a check that the simulation results for large samples agree with the
theoretical asymptotic distribution and hence a check on the programming of
the statistic.

David Jones




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