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Beta-Binomial Distribution

docs/tutorial:stats:discrete_betabinom

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

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

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

In the limiting case of $a = b = 1$ , the beta-binomial distribution reduces to a discrete uniform distribution:

f (k; n, 1, 1) = \frac{1}{n + 1}

In the limiting case of $n = 1$ , the beta-binomial distribution reduces to a Bernoulli distribution with the shape parameter $p = a / (a + b)$ :

f (k; 1, a, b) = {a / (a + b) b / (a + b) if k = 0 if k = 1

Implementation: scipy.stats.betabinom