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RE: st: Equality of distributions


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Equality of distributions
Date   Tue, 2 Nov 2004 19:04:52 -0000

Apart from the enormous caveat in Stas' statement, I'd 
recommend a strongly graphical approach, especially 
quantile-quantile plots, as giving various handles on 
this question. 

Single test statistics or attempts to identify a best 
distribution often miss important details: where doesn't it 
fit? In the tails? In the middle? etc. etc. 

Nick 
n.j.cox@durham.ac.uk 

Stas Kolenikov
 
> As far as I can recall, Kolmogorov-Smirnov test (Stata: ksmirnov) is
> the uniformly most powerful test for comparison of an empirical to
> fully known theoretical distributions, if there is no need to estimate
> the parameters of the latter. It cannot answer your second question
> though; it just says if the difference between the two distributions
> is within the limits of sampling fluctuations.

Nassar 

> > I have two distributions (observed) and several theoretical 
> (built upon
> > simulations), each is resumed into its own varaible (no expression)
> > I'm looking for tests in order to establish whether
> > - Reject/accept whether one theoretical distribution can 
> describe the
> > observed data..
> > - Given degrees of freedom, which one describe "best" the 
> observed data ?
> > References, commands in Stata are highly welcome..
> > 
> > Observed data are nominal, other are continuous

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