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Characterizations of Archimedean n -copulas

Włodzimierz Wysocki (2015)

Kybernetika

We present three characterizations of n -dimensional Archimedean copulas: algebraic, differential and diagonal. The first is due to Jouini and Clemen. We formulate it in a more general form, in terms of an n -variable operation derived from a binary operation. The second characterization is in terms of first order partial derivatives of the copula. The last characterization uses diagonal generators, which are “regular” diagonal sections of copulas, enabling one to recover the copulas by means of an...

Componentwise concave copulas and their asymmetry

Fabrizio Durante, Pier Luigi Papini (2009)

Kybernetika

The class of componentwise concave copulas is considered, with particular emphasis on its closure under some constructions of copulas (e.g., ordinal sum) and its relations with other classes of copulas characterized by some notions of concavity and/or convexity. Then, a sharp upper bound is given for the L ∞ -measure of non-exchangeability for copulas belonging to this class.

Conception et analyse de la forme limite d'une famille de coefficients statistiques d'association entre variables relationnelles. II

Israël-César Lerman (1992)

Mathématiques et Sciences Humaines

Cette étude offre une large vision de synthèse prospective ; mais aussi, des résultats techniques précis sur une famille très générale que nous avons élaborée de coefficients d'association entre variables descriptives relationnelles à partir de leur observation empirique sur un ensemble O d'objets élémentaires. Un même coefficient est obtenu à partir d'une forme de normalisation statistique par rapport à une hypothèse d'absence de liaison, d'un indice brut d'association. Ce dernier suppose une représentation...

Conception et analyse de la forme limite d'une famille de coefficients statistiques d'association entre variables relationnelles. 1ère partie

Israël-César Lerman (1992)

Mathématiques et Sciences Humaines

Cette étude offre une large vision de synthèse prospective : mais aussi, des résultats techniques précis sur une famille très générale que nous avons élaborée de coefficients d'association entre variables descriptives relationnelles à partir de leur observation empirique sur un ensemble O d'objets élémentaires. Un même coefficient est obtenu à partir d'une forme de normalisation statistique par rapport à une hypothèse d'absence de liaison, d'un indice brut d'association. Ce dernier suppose une représentation...

Congruences and ideals in lattice effect algebras as basic algebras

Sylvia Pulmannová, Elena Vinceková (2009)

Kybernetika

Effect basic algebras (which correspond to lattice ordered effect algebras) are studied. Their ideals are characterized (in the language of basic algebras) and one-to-one correspondence between ideals and congruences is shown. Conditions under which the quotients are OMLs or MV-algebras are found.

Constructing copulas by means of pairs of order statistics

Ali Dolati, Manuel Úbeda-Flores (2009)

Kybernetika

In this paper, we introduce two transformations on a given copula to construct new and recover already-existent families. The method is based on the choice of pairs of order statistics of the marginal distributions. Properties of such transformations and their effects on the dependence and symmetry structure of a copula are studied.

Constructing families of symmetric dependence functions

Włodzimierz Wysocki (2012)

Kybernetika

We construct two pairs ( 𝒜 F [ 1 ] , 𝒜 F [ 2 ] ) and ( 𝒜 ψ [ 1 ] , 𝒜 ψ [ 2 ] ) of ordered parametric families of symmetric dependence functions. The families of the first pair are indexed by regular distribution functions F , and those of the second pair by elements ψ of a specific function family ψ . We also show that all solutions of the differential equation d y d u = α ( u ) u ( 1 - u ) y for α in a certain function family α s are symmetric dependence functions.

Copula-based dependence measures

Eckhard Liebscher (2014)

Dependence Modeling

The aim of the present paper is to examine two wide classes of dependence coefficients including several well-known coefficients, for example Spearman’s ρ, Spearman’s footrule, and the Gini coefficient. There is a close relationship between the two classes: The second class is obtained by a symmetrisation of the coefficients in the former class. The coefficients of the first class describe the deviation from monotonically increasing dependence. The construction of the coefficients can be explained...

Copula-based grouped risk aggregation under mixed operation

Quan Zhou, Zhenlong Chen, Ruixing Ming (2016)

Applications of Mathematics

This paper deals with the problem of risk measurement under mixed operation. For this purpose, we divide the basic risks into several groups based on the actual situation. First, we calculate the bounds for the subsum of every group of basic risks, then we obtain the bounds for the total sum of all the basic risks. For the dependency relationships between the basic risks in every group and all of the subsums, we give different copulas to describe them. The bounds for the aggregated risk under mixed...

Copula–Induced Measures of Concordance

Sebastian Fuchs (2016)

Dependence Modeling

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. We present...

Corrélation entre variables nominales, ordinales, métriques ou numériques

Éric Térouanne (1998)

Mathématiques et Sciences Humaines

Un coefficient de corrélation est défini pour la distribution empirique conjointe de deux variables statistiques, que la structure a priori de chacune d'elles soit nominale, ordinale, métrique ou numérique. L'obtention d'un formalisme commun à toutes ces structures permet d'affiner l'analyse de la liaison entre les variables, en termes d'homogénéité (variables ordonnées), d'ordres sous-jacents (variables non-ordonnées) ou d'ordre induit (cas mixte).

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