# RE: st: Equality of distributions

 From "Nassar" <[email protected]> To <[email protected]> Subject RE: st: Equality of distributions Date Wed, 3 Nov 2004 10:50:09 +0100

```Nick & Stas

The test statistics are requested in order to figure on the QQplot..
Nothing else than the KS? I'm encountering some differences over the tails
- between LogNormal and Gamma distributions for my continuous observed data
- between GCPP (Generalized Compound Poisson Pascal, see Brocket & all
JMR1996) and NBD distribution for ordinal data

Best regards
Naji

-----Message d'origine-----
De : [email protected]
[mailto:[email protected]]De la part de Nick Cox
Envoy� : mardi 2 novembre 2004 20:05
� : [email protected]
Objet : RE: st: Equality of distributions

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
[email protected]

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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```

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