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Title: Multivariate Bernoulli distributions and discrete copulas Authors:  Elisa Perrone - Eindhoven University of Technology (Netherlands) [presenting]
Roberto Fontana - Politecnico di Torino (Italy)
Abstract: Multivariate Bernoulli distributions are used in many applied domains such as healthcare, social sciences, and finance. The class of $d$-dimensional Bernoulli distributions, with given Bernoulli univariate marginal distributions, admits a representation as a convex polytope. For exchangeable multivariate Bernoulli distributions with given margins, an analytical expression of the extreme points of the polytope has recently been determined. Discrete copulas are statistical tools to represent the joint distribution of discrete random vectors. They are fascinating mathematical objects that also admit a representation as a convex polytope. Studying polytopes of discrete copulas and their extreme points has recently gained attention in the literature. We explore potential connections between multivariate Bernoulli distributions, discrete copulas, and the extreme points of their associated polytopes. We discuss possible ways to unify the literature on the topics and describe some numerical examples.