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Beta-Negative Binomial Distribution

docs/tutorial:stats:discrete_betanbinom

The beta-negative binomial distribution is a negative binomial distribution with a probability of success p that follows a beta distribution. The probability mass function for betanbinom, defined for $k \geq 0$ , is:

f (k; n, a, b) = (k n + k - 1) \frac{B ( a + n , b + k )}{B ( a , b )}

for k in {0, 1,...}, where $B (a, b)$ is the Beta function.

In the limiting case of $n = 1$ , the beta-negative binomial distribution reduces to a beta-geometric distribution with the probability mass function:

f (k; a, b) = \frac{B ( a + 1 , b + k )}{B ( a , b )}

Implementation: scipy.stats.betanbinom