The aim of this manuscript is to determine the relative size of several functions (copulas, quasi–copulas) that are commonly used in stochastic modeling. It is shown that the class of all quasi–copulas that are (locally) associated to a doubly stochastic signed measure is a set of first category in the class of all quasi–copulas. Moreover, it is proved that copulas are nowhere dense in the clas...

In this paper, we present a class of multivariate copulas whose two-dimensional marginals belong to the family of bivariate Fréchet copulas. The coordinates of a random vector distributed as one of these copulas are conditionally independent.Weprove that thesemultivariate copulas are uniquely determined by their two-dimensional marginal copulas. Some other properties for thesemultivariate copul...

Based on the trivariate reduction technique two different trivariate Bernoulli mixtures of univariate uniform distributions and their associated trivariate copulas with bivariate linear Spearman marginal copulas are considered. Mathematical characterizations of these Bernoulli mixture models are obtained. Since Bernoulli mixture trivariate reduction copulas are not compatible with all valid gra...

Abstract Copulas are becoming a quite flexible tool in modeling dependence among the components of a multivariate vector. In order to predict extreme losses in insurance and finance, extreme value copulas and tail copulas play a more important role than copulas. In this paper, we review some estimation and testing procedures for both, extreme value copulas and tail copulas, which received much ...

Copulas are a useful tool to model multivariate distributions. While there exist various families of bivariate copulas, the construction of flexible and yet tractable copulas suitable for high-dimensional applications is much more challenging. This is even more true if one is concerned with the analysis of extreme values. In this paper, we construct a class of one-factor copulas and a family of...

This paper give some motivations for introducing copulas and presents some recent results on them. There is presented an application of copulas in the theory of aggregation operators. Transformations of copulas by means of increasing bijections on the unit interval and attractors of copulas are discussed. There is presented a result on an approximation of associative copulas by strict and nilpo...

Transformations of copulas by means of increasing bijections on the unit interval and attractors of copulas are discussed. The invariance of copulas under such transformations as well as the relationship to maximum attractors and Archimax copulas is investigated.

Archimedean copulas are copulas determined by a specific real function, called the generator. Composited with the copula at a given point, this generator can be expressed as a linear form of generators of the considered point components. In this paper, we discuss the case where this function is expressed as a quadratic form (called here multivariate Archimatrix copulas). This allows extending A...

The family of Liouville copulas is defined as the survival copulas of multivariate Liouville distributions, and it covers the Archimedean copulas constructed by Williamson’s d-transform. Liouville copulas provide a very wide range of dependence ranging from positive to negative dependence in the upper tails, and they can be useful in modeling tail risks. In this article, we study the upper tail...

Copulas have been popular to model dependence for multivariate distributions, but have not been used much in modelling temporal dependence of univariate time series. This paper shows some difficulties with using copulas even for Markov processes: some tractable copulas such as mixtures between copulas of complete coand countermonotonicity and independence (Fréchet copulas) are shown to imply qu...