Computer generation of negative binomial variates by envelope rejection

This paper proposes an envelope rejection method for computer sampling from the negative binomial distribution, with index parameter αα and probability parameter pp, based on a simple probability distribution inequality. Comparative timings with existing methods of generating NB variates show that the proposed method is comparable or faster when αα is not too large (α<11)(α<11), and it is fastest for all αα when p>0.7p>0.7.