Sklar's Theorem in an Imprecise Setting
Probability
2016-01-12 v1 Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.1601.02121,
title = {Sklar's Theorem in an Imprecise Setting},
author = {Ignacio Montes and Enrique Miranda and Renato Pelessoni and Paolo Vicig},
journal= {arXiv preprint arXiv:1601.02121},
year = {2016}
}
Comments
A definitive version has been published in a special issue on uncertainty and imprecision modelling in decision making (EUROFUSE 2013) of Fuzzy Sets and Systems