[R] extension of rnormp package

[Elio Mineo]

Il giorno mar, 24/07/2007 alle 06.39 +0100, Prof Brian Ripley ha
scritto:
> On Mon, 23 Jul 2007, Iwona Szyd?owska wrote:
> 
> > Hello,
> 
> > I would like to ask You, how to generate random numbers from an 
> > exponential power family with a shape parameter p less than 1(p->0). I 
> > found the rnormp package, which can generate numbers from this 
> > distribution, but only for parameter less or equal 1.
> 
> It seems you mean package 'normalp', and that the package author believes 
> that the exponential power distribution is only defined for p >= 1 
> (although that is not on the help page). Other authors believe it is 
> defined by a relationship to the gamma for all p > 0. So all you need to 
> do is to change the condition from p < 1 to p <= 0 in rnormp and friends.
> 
Well, I know that an exponential power distribution is defined for p>0,
(I think quite all the references I know consider p>0), but for 0<p<1
the algorithms that I have implemented for the estimates of the
distribution parameters and for the regression parameters are really
instable (pratically are not usable at all). Then, I prefered for all
the functions of the normalp package consider only the case p>=1.
All the best,
Angelo Mineo

> However, the algorithms used are not adequate for large or small p.  We 
> know that the distribution tends to uniform for p -> Inf, but pnormp and 
> rnormp break down for quite modest values of p.  As p -> 0 it tends to a 
> point distribution at 0, but you will see very large values far too often.
> So if you want p smaller than say 0.01 you will need to implement a 
> different algorithm.
> 
> >
> > Regards,
> >            Iwona Szydlowska
> > 	[[alternative HTML version deleted]]
> >
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