Sums of Possibly Associated Bernoulli Variables: The Conway–Maxwell-Binomial Distribution

Abstract

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 (CMB) distribution gracefully models both positive and negative association. This distribution has sufficient statistics and a family of proper conjugate distributions. The relationship of this distribution to the exchangeable special case is explored, and two applications are discussed.