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 [ [email protected] | http://purl.org/stefan.evert ]
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