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Title: Diagonal distributions Authors:  Miguel de Carvalho - CEAUL (Centro de Estatistica e Aplicacoes), Universidade de Lisboa (Portugal) [presenting]
Manuele Leonelli - University of Glasgow (United Kingdom)
Rodrigo Rubio - Pontificia Universidad Catolica de Chile (Chile)
Abstract: Diagonal distributions are introduced as an extension of marginal distributions. The main diagonal will be examined in detail, which consists of a mean-constrained univariate distribution on $[0, 1]$, that summarizes key features on the dependence structure, and whose variance connects to Spearman's rho. We will comment on $D$-dimensional extensions, and on the fact that in the case of independence there is a connection with the so-called Irwin--Hall distribution. Mean-constrained histograms and smoothing methods are developed so to learn about diagonal distributions. Real and simulated data will be used in order to illustrate the key concepts and methods.