Sklar's Theorem in an Imprecise Setting

Ignacio Montes, Enrique Miranda, Renato Pelessoni, Paolo Vicig

Published 2016-01-09Version 1

Sklar's theorem is an important tool that connects bidimensional distribution functions with their marginals by means of a copula. When there is imprecision about the marginals, we can model the available information by means of p-boxes, that are pairs of ordered distribution functions. Similarly, we can consider a set of copulas instead of a single one. We study the extension of Sklar's theorem under these conditions, and link the obtained results to stochastic ordering with imprecision.