  The study of sums of possibly associated Bernoulli random variables has been
hampered by an asymmetry between positive correlation and negative correlation.
The Conway-Maxwell Binomial (COMB) distribution and its multivariate extension,
the Conway-Maxwell Multinomial (COMM) distribution, gracefully model both
positive and negative association. Sufficient statistics and a family of proper
conjugate distributions are found. The relationship of this distribution to the
exchangeable special case is explored, and two applications are discussed.
