The beta-binomial is a discrete distribution on 0, 1, ..., *n* where the probability of success in a binomial distribution (*p*) is itself drawn from a beta distribution.

The beta-binomial disribution is a discrete distribution on 0, 1, ..., n.

It arises as a mixture distribution, where the probability of success in a binomial distribution (p) is itself drawn from a beta distribution. Because of this it is sometimes used as a model for heterogeneous mixtures of binomials or more generally for situations where the variance of a discrete distribution on 0, 1, ..., n has a larger variance than the binomial.

It also commonly occurs in Bayesian applications.

Reference: Wikipedia - Beta-binomial distribution

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