Séminaire du CIMMUL | Patrizia Semeraro

The Bernoulli structure of discrete distributions and applications

Patrizia Semeraro
Politecnico di Torino

Résumé

We provide a geometrical structure for classes of high dimensional Bernoulli distributions that turns out to be important to address open issues such as dependence or aggregate risk. We focus on the class of Bernoulli variables X = (X1,…,Xd) with given margins and the class P(p) of d-dimensional Bernoulli variables X the sum of which Pd i=1 Xi have the same distribution p. We prove that they are convex polytopes and we nd their extremal points. Our characterization allows us to nd bounds for dependence as well as risk measures. However, our main result is to prove that the Hausdor measure of the polytopes P(p) is the density l(p) over the simplex of discrete distributions D of a nite measure s that is Hausdor  absolutely continuous. We also prove that the measure s normalized over the simplex D belongs to the class of Dirichlet distributions.

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Le séminaire aura lieu au local 3820 du pavillon Alexandre-Vachon et en ligne.

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