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.
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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--
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595