It reduces to the Bernoulli distribution as a special case when "n" = 1. For "α" = "β" = 1, it is the discrete uniform distribution from 0 to "n". It also approximates the binomial distribution arbitrarily well for large "α" and "β". Similarly, it contains the negative binomial distribution in the limit with large "β" and "n". The beta-binomial is a one-dimensional version of the Dirichlet-multinomial distribution as the binomial and beta distributions are univariate versions of the multinomial and Dirichlet distributions respectively.