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Representation of discrete quasi-copulas through non-square matrices
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In this paper a matrix representation for discrete quasi-copulas defined on a non-square grid In× Imof [0,1]2with m=kn, k≥1 is given. The special case of irreducible discrete quasi-copulas (those that cannot be expressed as nontrivial convex combination of other ones) is also studied. It is proved that quasi-copulas of minimal range admit a matrix representation through a special class of matrices. In the case of copulas, it is proved that irreducible copulas coincide with those of minimal range. Moreover, an algorithm to express any discrete copula as a convex combination of irreducible ones is given.
Title: Representation of discrete quasi-copulas through non-square matrices
Description:
In this paper a matrix representation for discrete quasi-copulas defined on a non-square grid In× Imof [0,1]2with m=kn, k≥1 is given.
The special case of irreducible discrete quasi-copulas (those that cannot be expressed as nontrivial convex combination of other ones) is also studied.
It is proved that quasi-copulas of minimal range admit a matrix representation through a special class of matrices.
In the case of copulas, it is proved that irreducible copulas coincide with those of minimal range.
Moreover, an algorithm to express any discrete copula as a convex combination of irreducible ones is given.
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