negative binomial distribution
NB(r, p) is the number of times you do thing with success probability p until you get r successes. (Sometimes p is probability of failure? Just depends on the package you are using)
So NB(5, 1/6) is the distribution of times you have to roll a 6 sided die before you get 5 6s
General case of the geometric distribution (geom(p) = NB(1, p))
to do hypothesis testing and see if two negative binomial distributions are different, I suggest generalized linear models in R, specifically glm.nb
