[R] Statistical question re assessing fit of distribution functions.

David Scott d.scott at auckland.ac.nz
Tue Sep 23 23:27:23 CEST 2008

On Tue, 23 Sep 2008, Ted Byers wrote:

> Thanks Timur
> While assessing whether or not the best option would be a normal
> distribution (it won't be, the data in this case LOOKS more poisson, or if I
> explude the first week of results, a negative exponential; and in my other
> case, cauchy is more likely), I really need a test that can be applied
> regardless of the distribution to see which distribution fits best.  Using
> log-likelihood, there doesn't seem to be much to choose between exponential
> and poisson (the log-likelihhod for them being almost the same, regardless
> of the sample even tough the parameters are very different from one sample
> to the next - I don't understand why yet), and the others I have tried are
> MUCH worse, but I'm not done yet.
> Are you aware of functions that allow estimation of all the parameters of a
> non-central distribution?  I ask because a problem I'll be working on in a
> few weeks will involve the kind of skew produced by a non-central
> distribution (among others).  I see some functions allow you to work with
> skewed distributions (e.g. "[dpqr]stable  the skewed stable distribution ")
> but I have not yet found functions that alow one to estimate their
> parameters from real data.
> Thanks,
> Ted


You have talked about heavy tailed, skewed distributions. To fit these 
you need to look at some packages. There are a number of possibilities in 
fBasics which is part of Rmetrics, sn is a very nice package for the skew 
normal and skew t distributions, and there are packages for the hyperbolic 
and generalized hyperbolic distributions: HyperbolicDist, ghyp and QRMlib.

You won't find much on goodness of fit tests I think. I have an 
implementation of the Cramer-von Mises test for the hyperbolic in my 
package (HyperbolicDist) but I am not aware of a lot else being available.

David Scott

David Scott	Department of Statistics, Tamaki Campus
 		The University of Auckland, PB 92019
 		Auckland 1142,    NEW ZEALAND
Phone: +64 9 373 7599 ext 86830		Fax: +64 9 373 7000
Email:	d.scott at auckland.ac.nz

Graduate Officer, Department of Statistics
Director of Consulting, Department of Statistics

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