  The beta distribution is a basic distribution serving several purposes. It is
used to model data, and also, as a more flexible version of the uniform
distribution, it serves as a prior distribution for a binomial probability. The
bivariate beta distribution plays a similar role for two probabilities that
have a bivariate binomial distribution. We provide a new multivariate
distribution with beta marginal distributions, positive probability over the
unit square, and correlations over the full range. We discuss its extension to
three or more dimensions.
