Beta negative binomial distribution

In probability theory, a beta negative binomial distribution is the probability distribution of a discrete random variable X {\displaystyle X} equal to the number of failures needed to get r {\displaystyle r} successes in a sequence of independent Bernoulli trials. The probability p {\displaystyle p} of success on each trial stays constant within any given experiment but varies across different experiments following a beta distribution.

Source: Wikipedia — Beta negative binomial distribution (CC BY-SA 4.0)