Re: st: Re: Random draws from a negative binomial distribution

[Dirk Enzmann <dirk.enzmann@uni-hamburg.de>]

Thanks to Andrew, Kieran and Timothy for their helpful comments and to 
StataCorp for solving this problem so quickly!

Kieran showed a workaround to the -rpoisson- limit that may work for 
rough estimates and Timothy provided a very useful link to details on 
programming the simulation of Poisson variables.

StataCorp and the Stata community are really amazing!

Dirk

At Wed, 19 Jun 2013 15:33:56 -0500, rgates@stata.com (Richard Gates, 
StataCorp) wrote:
> Dirk Enzmann has tickled a domain limit of Stata's -rnbinomial()- function.
>
> He states:
>
> > >  Unfortunately, I am not able to solve the following problem in Stata
> > >  which I can solve easily using R:
> > >
> > >  As far as I can see Stata does not allow to draw random values from a
> > >  negative binomial distribution if "size" (= 1/alpha) is less than 0.1
> > >  (see -h rnbinomial-). I tried to circumvent this problem by (1) creating
> > >  random draws from a gamma distribution with shape parameter = size and
> > >  scale parameter = (1-prob)/prob, with prob = size/(size+mu), and
> > >  subsequently creating random draws from a poisson distribution with
> > >  parameter m = the result of the previous random draws from the gamma
> > >  distribution. However, if size is small, this does not help either.
> We have determined that the domain limit for the size parameter, labeled as n
> in Stata's documentation, is too conservative for a certain region of the
> parameter space, when n<0.1 but n*(1-p)/p<100 and p^n>1e-4.  Dirk's example
> falls into this region.  We will update -rnbinomial()- in Stata 12 and Stata
> 13 to produce a result in this region.
>
>
> - -- Rich
> rgates@stata.com

--
========================================
Dr. Dirk Enzmann
Institute of Criminal Sciences
Dept. of Criminology
Rothenbaumchaussee 33
D-20148 Hamburg
Germany

phone: +49-(0)40-42838.7498 (office)
       +49-(0)40-42838.4591 (Mrs Billon)
fax:   +49-(0)40-42838.2344
email: dirk.enzmann@uni-hamburg.de
http://www2.jura.uni-hamburg.de/instkrim/kriminologie/Mitarbeiter/Enzmann/Enzmann.html
========================================
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