Sklar's Theorem in Finite Settings

Authors:
G. Mayor;J. Suner;J. Torrens
Affiliations:
Univ. of the Balearic Islands, Palma de Mallorca;-;-
Venue:
IEEE Transactions on Fuzzy Systems
Year:
2007

Citing 0
Cited 3

Matrix representation of discrete quasi-copulas

Fuzzy Sets and Systems
Representation of discrete quasi-copulas through non-square matrices

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Matrix representation of copulas and quasi-copulas defined on non-square grids of the unit square

Fuzzy Sets and Systems

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Abstract

This paper deals with the well-known Sklar's theorem, which shows how joint distribution functions are related to their marginals by means of copulas. The main goal is to prove a discrete version of this theorem involving copula-like operators defined on a finite chain, that will be called discrete copulas. First, the idea of subcopulas in this finite setting is introduced and the problem of extending a subcopula to a copula is solved. This is precisely the key point which allows to state and prove the discrete version of Sklar's theorem.