Related papers: Copulas: compatibility and Fr\'echet classes

We study a broad class of asymmetric copulas introduced by Liebscher (2008) as a combination of multiple - usually symmetric - copulas. The main thrust of the paper is to provide new theoretical properties including exact tail dependence…

We propose a semiparametric family of copulas based on a set of orthonormal functions and a matrix. This new copula permits to reach values of Spearman's Rho arbitrarily close to one without introducing a singular component. Moreover, it…

There exist many bivariate parametric copulas to model bivariate data with different dependence features. We propose a new bivariate parametric copula family that cannot only handle various dependence patterns that appear in the existing…

We show that the lower and upper Frech\'{e}t-Hoeffding copulas, which are singular, can be regularized to absolutely continuous copulas. The method, which is constructive and explicit, states sufficient conditions for when an absolutely…

In this article, the concept of copulas is generalised to infinite dimensional Hilbert spaces. We show one direction of Sklar's theorem and explain that the other direction fails in infinite dimensional Hilbert spaces. We derive a necessary…

Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. More recently, they have been applied to solve statistical…

We express each Fr\'echet class of multivariate Bernoulli distributions with given margins as the convex hull of a set of densities, which belong to the same Fr\'echet class. This characterisation allows us to establish whether a given…

The class of index-mixed copulas is introduced and its properties are investigated. Index-mixed copulas are constructed from given base copulas and a random index vector, and show a rather remarkable degree of analytical tractability. The…

This paper introduces a new class of Cox models for dependent bivariate data. The impact of the covariate on the dependence of the variables is captured through the modification of their copula. Various classes of well known copulas are…

This paper proposes multivariate copula models for hierarchical data. They account for two types of correlation: one is between variables measured on the same unit and the other is a correlation between units in the same cluster. This model…

We give derivations of some basic results for the Bernstein approximation in $n$ variables that are useful in investigating copulas. It is shown that Bernstein approximations of copulas are again copulas. We exhibit a stochastic…

Tests of equality of copulas between two samples are introduced and studied using the empirical Bernstein copula process. Three statistics are proposed and their asymptotic properties are established. Besides, a subsampling Bernstein…

In probability and statistics, copulas play important roles theoretically as well as to address a wide range of problems in various application areas. In this paper, we introduce the concept of multivariate discrete copulas, discuss their…

We extend the classification of mixed states of quantum systems composed of arbitrary number of subsystems of arbitrary dimensions. This extended classification is complete in the sense of partial separability and gives 1+18+1 partial…

We give a topological bound on the number of minimal models of a class of three dimensional log smooth pairs of general type.

Vine copulas are a highly flexible class of dependence models, which are based on the decomposition of the density into bivariate building blocks. For applications one usually makes the simplifying assumption that copulas of conditional…

It is shown that an ensemble of particles with tripolar (colour) charges will necessarily cohere in a hierarchy of structures, from simple clusters and strings to complex aggregates and cyclic molecule-like structures. The basic…

In this paper, we construct a bound copula, which can reach both Frechet's lower and upper bounds for perfect positive and negative dependence cases. Since it covers a wide range of dependency and simple for computational purposes, it can…

We collect well known and less known facts about the bivariate normal distribution and translate them into copula language. In addition, we prove a very general formula for the bivariate normal copula, we compute Gini's gamma, and we…

Copulas are a powerful tool to model dependence between the components of a random vector. One well-known class of copulas when working in two dimensions is the Farlie-GumbelMorgenstern (FGM) copula since their simple analytic shape enables…