In this paper we characterize the concept of quasi-copula in three different ways: as a special subclass of aggregation operators, in terms of its associated volume and—for the bivariate case—in ...terms of non-increasing tracks on
0
,
1
2
. We also provide sufficient conditions and new properties for quasi-copulas.
If H denotes the joint distribution function of n random variables X
1
, X
2
,..., X
n
whose margins are F
1
, F
2
,..., F
n
, respectively, then the fundamental best-possible bounds inequality for H ...is
F
2
(x
2
),..., F
n
(x
n
)) for all x
1
, x
2
,..., x
n
in −∞, ∞. In this paper we employ n-copulas and n-quasi-copulas to find similar bounds on arbitrary sets of multivariate distribution functions with given margins. We discuss bounds for an n-quasi-copula Q when a value of Q at a single point is known. As an application, we investigate about bounds for a multivariate distribution function H with given univariate margins when the value of H is known at a single point whose coordinates are percentiles of the variables X
1
, X
2
,..., X
n
, respectively.
A new class of symmetric bivariate copulas Durante, Fabrizio
Journal of nonparametric statistics,
10/1/2006, 2006-10-00, 20061001, Letnik:
18, Številka:
7-8
Journal Article
Recenzirano
A new class of copulas, depending on a univariate function, is studied and its properties (dependence, ordering, measures of association, symmetry) are investigated.
In this note we provide a large class of diagonals for which the best-possible upper bound on sets of copulas with a given diagonal section is a copula.
In this paper smooth aggregation functions on a finite scale are studied and characterized as solutions of a functional equation analogous to the Frank functional equation. The particular cases of ...quasi-copulas and copulas are also characterized through a similar functional equation. Previous characterizations of these kind of operations through special matrices are used jointly with the new ones to derive some invariant properties on quasi-copulas and copulas on finite scales.
In the paper the structure of quasi-copulas on discrete scales is studied. A special attention is given to the study of quasi-copulas with diagonal section. The cardinality of the set of ...quasi-copulas on L(n) determined univocally by the corresponding diagonal section is shown to be the Fibonacci number pn.
It is well known that every bivariate copula induces a positive measure on the Borel σ-algebra on 0,12, but there exist bivariate quasi-copulas that do not induce a signed measure on the same ...σ-algebra. In this paper we show that a signed measure induced by a bivariate quasi-copula can always be expressed as an infinite combination of measures induced by copulas. With this we are able to give the first characterization of measure-inducing quasi-copulas in the bivariate setting.
We correct the formula for the best-possible upper bound on the set of copulas with a given value of the Spearman's footrule coefficient recently published in 1.
In this paper, we introduce patchwork constructions for multivariate quasi-copulas. These results appear to be new since the kind of approach has been limited to either copulas or only bivariate ...quasi-copulas so far. It seems that the multivariate case is much more involved, since we are able to prove that some of the known methods of bivariate constructions cannot be extended to higher dimensions. Our main result is to present the necessary and sufficient conditions both on the patch and the values of it for the desired multivariate quasi-copula to exist. We also give all possible solutions.
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