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Sklar's Theorem in Finite Settings

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3 Author(s)
Mayor, G. ; Univ. of the Balearic Islands, Palma de Mallorca ; Suner, J. ; Torrens, J.

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.

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Fuzzy Systems, IEEE Transactions on  (Volume:15 ,  Issue: 3 )