The theory of positive dependence notions cannot yield useful results for some widely used distributions such as the multinomial, Dirichlet and the multivariate hypergeometric. Some conditions of negative dependence that are satisfied by these distributions and which have practical meaning are introduced. Useful inequalities for some widely used distributions are obtained.
"Some Concepts of Negative Dependence." Ann. Probab. 10 (3) 765 - 772, August, 1982. https://doi.org/10.1214/aop/1176993784