Conway--Maxwell multivariate Bernoulli distribution

We investigate the Conway–Maxwell multivariate Bernoulli distributions, a family of multivariate Bernoulli distributions derived from the Conway–Maxwell-binomial distribution. We show that it is possible to set the parametrization such that the Bernoulli marginals remain intact, allowing us to study dependence properties within this family. In particular, we demonstrate that this family spans the full spectrum of dependence. Moreover, for specific ranges of the parameters, these distributions satisfy the strongly Rayleigh property, a negative dependence notion stronger than negative association.