Date: Sep 22, 2012 10:24 AM
Author: Luis A. Afonso
Subject: Re: Kolmogorov-Smirnov-Lilliefors Test statistics

An only descriptive item on the Lilliefors statistics 


Result: with growing normal sample sizes N the Kolmogorov-Smirnov- Lilliefors one-sample test statistics tends to be inside the interval [0.10, 0.20): approximately 95 % for sizes 350, 98% to 99% for 600 and beyond, using 10´000 samples each size.
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TABLE. Distribution of Lilliefors statistics among intervals for normal data

_____________[0.00, 0.10)___[0.10, 0.20)___[0.20, 0.30)

__N=250______12.34%_______87.34________0.32___
____ 300_______7.91________ 91.68________0.41___
____ 350_______4.86________ 94.80________0.34___
____ 400_______3.31________ 96.19________0.50___
____ 500_______1.28________ 97.96________0.76___


____ 600_______0.63________ 98.48________0.89___
____ 700_______0.22________ 98.80________0.98___
____ 800_______0.06________ 98.69________1.25___
____ 900_______0.08________ 98.61________1.31___
___ 1000_______0.02________ 98.50________1.48___


Note low statistics, 10´000 samples, is not an adequate choice. In consequence the second decimal place of the [0.10, 0.20) target interval should be taken with reserve, even the first varies from 5 to 8, n=500 onwards. One can see that the firth interval contents becomes smaller whereas the third grows.



Luis A. Afonso



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