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

[rgates@stata.com (Richard Gates, StataCorp)]

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
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/