This paper introduces a model called "Beta-Geometric / NBD" which models "repeat-buying behavior in settings where customer “dropout” is unobserved: It assumes that customers buy at a steady rate (albeit in a stochastic manner) for a period of time, and then become inactive."
While I understand the "Beta-Geometric" aspects of the model (the number of purchases until a user becomes inactive, with Beta modeling heterogeneity across users), I don't quite get what NBD really refers to in this model.
NBD supposedly stands for Negative Binomial, but what's negative binomial about this model? I read online that it's related to having a Poisson-Gamma mixture, which this model has, but why? What's the connection between Negative Binomial and a Poisson Gamma mixture? If that's not the connection, why does the model name emphasize the term NBD?
I list the model assumptions below.