Extremal negative dependence and the strongly Rayleigh property

Hélène Cossette; Etienne Marceau; Alessandro Mutti; Patrizia Semeraro

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arXiv · 2504.17679

Extremal negative dependence and the strongly Rayleigh property

Hélène Cossette·Etienne Marceau·Alessandro Mutti·Patrizia Semeraro

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Abstract

We provide a geometrical characterization of extremal negative dependence as a convex polytope in the simplex of multidimensional Bernoulli distributions, and we prove that it is an antichain that satisfies some minimality conditions with respect to the strongest negative dependence orders. We study the strongly Rayleigh property within this class and explicitly find a distribution that satisfies this property by maximizing the entropy. Furthermore, we construct a chain for the supermodular order starting from extremal negative dependence to independence by mixing the maximum entropy strongly Rayleigh distribution with independence.

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Hélène Cossette, Etienne Marceau, Alessandro Mutti, Patrizia Semeraro. 2025-04-24. Extremal negative dependence and the strongly Rayleigh property. https://arxiv.org/abs/2504.17679

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