Conway--Maxwell multivariate Bernoulli distribution

TL;DR

This paper introduces the Conway--Maxwell multivariate Bernoulli distribution family, exploring its dependence properties and conditions for negative dependence, including the strongly Rayleigh property.

Contribution

It characterizes the dependence spectrum of this distribution family and identifies parameter ranges for negative dependence properties.

Findings

The family spans the full spectrum of dependence.

Certain parameter ranges satisfy the strongly Rayleigh property.

The marginals remain intact under specific parametrizations.

Abstract

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.