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Topic: Kolmogorov-Smirnov-Lilliefors Test statistics
Replies: 10   Last Post: Jun 8, 2013 7:39 PM

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Luis A. Afonso

Posts: 4,615
From: LIsbon (Portugal)
Registered: 2/16/05
Critical values of Lilliefors Dmax, D2max, N=100
Posted: Jun 4, 2013 5:21 PM
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Critical values of Lilliefors Dmax, D2max, N=100

(D2max= secondary test statistics maximum)

_____n=100 / 400´000_
__________Two experiments I, II
_alpha______Dmax___D2max___
_0.20_______0.0736__0.0695___
___________ 0.0736__0.0695___
_0.15_______0.0770__0.0730___
___________ 0.0770__ 0.0729___
_0.10_______0.0816__0.0775___
___________ 0.0816__ 0.0775___
_0.05_______0.0888__0.0847___
___________ 0.0889__0.0847___
_0.01_______0.1034__0.0991___
___________ 0.1034__0.0990___
Considering literature not unworthy / futile try to calculate the Lilliefors critical value for n=100. In fact Tables from H. Abdil ? P. Molin does stop in what concerns direct / simulation at size 50, the number of samples k=100´000. Beyond this value they provide an global formula for whatever size. Relative to 5% and 1% they obtained
___c(5%) = 0.895/fn_____fn=(.83+n)/sqrt(n) ? 0.01
___c(1%) = 1.035/fn
Resulting the critical values 0.0889, 0.1027 respectively.
From my simulations, k=400´000 did result (2 experiments):
__5%___0.0888, 0.0889___D2max__0.0847, 0.0847
__1%___0.1034, 0.1034__________ 0.0991, 0.0990
The agreement is not so good for 1%. These values will be useful for further application/numeric example . . .
Bibl.
Lilliefors/Van Soest´s test of normality, H. Abdil, Paul Molin, Encyclopedia of Measurement and Statistics.
wwwpub.utdallas.edu/~herve/Abdi-Lillie2007-pretty.pdf
Luis A. Afonso



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