The Beta-Binomial Distribution

Abstract

The beta-binomial distribution can be thought of as a binomial distribution where the probability of success in each trial is not fixed but follows a beta distribution. It is often used to capture correlation in a sequence of Bernoulli trials or to model over-dispersion. Furthermore, it frequently arises in Bayesian statistics, since the beta distribution is the conjugate prior of the Bernoulli distribution. This article is a tutorial on the beta-binomial distribution, its connection with other distributions, its derivation and properties. Several examples are given and common misunderstandings addressed.