[R] Kolmogorov-Smirnof test for lognormal distribution with estimated parameters

[Christoph Buser]

Hi Kwabena

I did once a simulation, generating normal distributed values
(500 values) and calculating a KS test with estimated
parameters. For 10000 times repeating this test I got about
1 significant tests (on a level alpha=0.05 I'm expecting about 500 
significant tests by chance)
So I think if you estiamte the parameters from the data, you fit
to good and the used distribution of the test statistic is not
adequate as it is indicated in the help page you cited. There
(in the help page) is some literature, but it is no easy stuff
to read.
Furthermore I know no implementation of an KS test which
accounts for this estimation of the parameter.

I recommend a graphical tool instead of a test:

x <- rlnorm(100)
qqnorm(log(x))

See also ?qqnorm and ?qqplot.

If you insist on testing a theoretical distribution be aware
that a non significant test does not mean that your data has the
tested distribution (especially if you have few data, there is
no power in the test to detect deviations from the theoretical
distribution and the conclusion that the data fits well is
trappy)

If there are enough data I'd prefer a chi square test to the KS
test (but even there I use graphical tools instead). 

See ?chisq

For this test you have to specify classes and this is 
subjective (you can't avoid this).

You can reduce the DF of the expected chi square distribution
(under H_0) by the number of estimated parameters from the data
and will get better results. 

DF = number of classes - 1 - estimated parameters

I think this test is more powerful than the KS test,
particularly if you must estimate the parameters from data.

Regards,

Christoph

-- 
Christoph Buser <buser at stat.math.ethz.ch>
Seminar fuer Statistik, LEO C11
ETH (Federal Inst. Technology)	8092 Zurich	 SWITZERLAND
phone: x-41-1-632-5414		fax: 632-1228
http://stat.ethz.ch/~buser/



Kwabena Adusei-Poku writes:
 > Hello all,
 > 
 > Would somebody be kind enough to show me how to do a KS test in R for a
 > lognormal distribution with ESTIMATED parameters. The R function
 > ks.test()says "the parameters specified must be prespecified and not
 > estimated from the data" Is there a way to correct this when one uses
 > estimated data?
 > 
 > Regards,
 > 
 > Kwabena.
 > 
 > --------------------------------------------
 > Kwabena Adusei-Poku
 > University of Goettingen
 > Institute of Statistics and Econometrics
 > Platz der Goettingen Sieben 5
 > 37073 Goettingen
 > Germany
 > Tel: +49-(0)551-394794
 > 
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