  We discuss a bivariate beta distribution that can model arbitrary
beta-distributed marginals with a positive correlation. The distribution is
constructed from six independent gamma-distributed random variates. We show how
the parameters of the distribution can be fit to data using moment matching.
Previous work used an approximate and sometimes inaccurate method to compute
the covariance. Here, we derive all product moments and the exact covariance,
which can easily be computed numerically. The bivariate case can be generalized
to a multivariate distribution with arbitrary beta-distributed marginals.
Furthermore, we generalize the distribution from two marginal beta to two
marginal Dirichlet distributions. The resulting correlated Dirichlet
distribution makes it possible to model two correlated Dirichlet-distributed
random vectors.
