[R-lang] GIGP - random sample? CDF?

[Stefan Evert]

Hi David!

> I have collocation data that fits the Generalized Inverse Gaussian- 
> Poisson distribution quite well (via the ZipfR package).  Now I'd  
> like to randomly sample from such a distribution.  Does anyone know  
> how to do that?

There's a reason why zipfR doesn't offer a random sample generator for  
GIGP models: my (straightforward) implementation of random sampling  
transforms uniform random numbers into LNRE-distributed types using  
the quantile function (i.e. the inverses of the cumulative  
distribution function) and the cumulative type distribution function.   
Since ...

> For starters, I could probably do with an integral-free cumulative  
> distribution function for a GIGP, as that would get me 3/4 of the  
> way there.

... I'm not aware of any closed-form expression (or even taylor  
expansions or such) for incomplete integrals of the GIGP density  
function, I haven't implemented these functions yet.  The complete  
integrals (from 0 to +inf) have closed-form expressions involving  
Bessel functions, given in Baayen (2001).

BTW, this is one of the main reasons why I prefer the simplistic ZM/ 
fZM models over GIGP.

> (I can think of some iterative/numerical way, but that wouldn't be  
> very elegant - I might as well sample from the corpus data in that  
> case.)

Exactly.  I would stay away from numerical integration in this case.   
Your goal is probably to run simulation experiments, so you will need  
a large number of random draws, and each of this would require to  
calculate several numerical integrals with high precision (this is  
essential for the transformation from a uniform distribution to a LNRE  
distribution).

I've toyed with the possibility of using rejection sampling or a  
similar approach for GIGP, but haven't found a feasible solution yet.   
Any suggestions (or code :-) are highly welcome.


Best regards,
Stefan Evert

[ stefan.evert at uos.de | http://purl.org/stefan.evert ]



-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://pidgin.ucsd.edu/pipermail/r-lang/attachments/20090409/302b45e7/attachment-0001.htm>