Displaying similar documents to “N-dimensional measures of dependence.”

On measures of concordance.

Marco Scarsini (1984)

Stochastica

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We give a general definition of concordance and a set of axioms for measures of concordance. We then consider a family of measures satisfying these axioms. We compare our results with known results, in the discrete case.

On independence in some families of multivariate distributions.

José Juan Quesada (1986)

Stochastica

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In this paper we will prove a characterization for the independence of random vectors with positive (negative) orthant dependence according to a direction. The result can be seen as a generalization of a result by Lehmann [4].

Copula–Induced Measures of Concordance

Sebastian Fuchs (2016)

Dependence Modeling

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We study measures of concordance for multivariate copulas and copulas that induce measures of concordance. To this end, for a copula A, we consider the maps C → R given by [...] where C denotes the collection of all d–dimensional copulas, M is the Fréchet–Hoeffding upper bound, Π is the product copula, [. , .] : C × C → R is the biconvex form given by [C, D] := ∫ [0,1]d C(u) dQD(u) with the probability measure QD associated with the copula D, and ψΛ C → C is a transformation of copulas....

A Biconvex Form for Copulas

Sebastian Fuchs (2016)

Dependence Modeling

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We study the integration of a copula with respect to the probability measure generated by another copula. To this end, we consider the map [. , .] : C × C → R given by [...] where C denotes the collection of all d–dimensional copulas and QD denotes the probability measures associated with the copula D. Specifically, this is of interest since several measures of concordance such as Kendall’s tau, Spearman’s rho and Gini’s gamma can be expressed in terms of the map [. , .]. Quite generally,...

Generalized normal distributions.

Robert M. Tardiff (1980)

Stochastica

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It is well known (see [2], p. 158) that if X and Y are independent random variables with a continuous joint probability density function (pdf) which is spherically symmetric about the origin, then both X and Y are normally distributed. In this note we examine the condition that the joint pdf be spherically symmetric about the origin and show that the normal distribution is strongly dependent on the choice of metric for R.

Representation of continuous associative functions.

Barbara Baccheli (1986)

Stochastica

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Strengthened forms of Ling's representation theorem concerning a class of continuous associative functions are given: Firstly the monotonicity condition is removed. Then the associativity condition is replaced by the power associativity.

Some remarks on a problem of C. Alsina.

J. Matkowski, M. Sablik (1986)

Stochastica

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Equation [1] f(x+y) + f (f(x)+f(y)) = f (f(x+f(y)) + f(f(x)+y)) has been proposed by C. Alsina in the class of continuous and decreasing involutions of (0,+∞). General solution of [1] is not known yet. Nevertheless we give solutions of the following equations which may be derived from [1]: [2] f(x+1) + f (f(x)+1) = 1, [3] f(2x) + f(2f(x)) = f(2f(x + f(x))). Equation [3] leads to a Cauchy functional equation: ...