For our model, note that Negative Binomial is obtained from a Poisson distribution Po(λ) whose parameter λ again follows a Gamma distribution Ga(r, b) and integrated out: This construction exactly mirrors the Poisson-Gamma word length distribution in (Mochihashi et al., 2009) with sampled λ.
our Negative Binomial is basically a continuous analogue of the word length distribution in NPYLM.