Sklar's Theorem in an Imprecise Setting

Ignacio Montes; Enrique Miranda; Renato Pelessoni; Paolo Vicig

doi:10.1016/j.fss.2014.10.007

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arXiv · 1601.02121

Sklar's Theorem in an Imprecise Setting

Ignacio Montes·Enrique Miranda·Renato Pelessoni·Paolo Vicig

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Abstract

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.

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Ignacio Montes, Enrique Miranda, Renato Pelessoni, Paolo Vicig. 2016-01-09. Sklar's Theorem in an Imprecise Setting. https://doi.org/10.1016/j.fss.2014.10.007

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