Abstract. We consider copulas with a given diagonal section and compute the explicit density of the unique optimal copula which maximizes the entropy. In this sense, this copula is the least informative among the copulas with a given diagonal section. We give an explicit criterion on the diagonal section for the existence of the optimal copula and give a closed formula for its entropy. We also ...

One of the most computationally convenient non-redundant ways to describe the dependence between two variables is by describing the corresponding copula. In many application, a special class of copulas – known as FGM copulas – turned out to be most successful in describing the dependence between quantities. The main result of this paper is that these copulas are the fastest-to-compute, and this...

This paper suggests to use Lévy copulas to characterize the dependence among components of multidimensional Lévy processes. This concept parallels the notion of a copula on the level of Lévy measures. As for random vectors, a kind of Sklar’s theorem states that the law of a general multivariate Lévy process is obtained by combining arbitrary univariate Lévy processes with an arbitrary Lévy copu...

We review the main “omnibus procedures” for goodness-of-fit testing for copulas: tests based on the empirical copula process, on probability integral transformations, on Kendall’s dependence function, etc, and some corresponding reductions of dimension techniques. The problems of finding asymptotic distribution-free test statistics and the calculation of reliable p-values are discussed. Some pa...

Copulas are functions that describe the dependence between two or more random variables. This article provides a brief review of copula theory and two areas of economics in which copulas have played important roles: multivariate modeling and partial identification of parameters that depend on the joint distribution of two random variables with fixed or knownmarginal distributions.We focus on bi...

Tail dependence copulas provide a natural perspective from which one can study the dependence in the tail of a multivariate distribution. For Archimedean copulas with continuously differentiable generators, regular variation of the generator near the origin is known to be closely connected to convergence of the corresponding lower tail dependence copulas to the Clayton copula. In this paper, th...

There are several theorical results about order statistics and copulas in the literature that have  been mentioned also by Nelsen cite{p20}. The present study after reviewing some of these results, relies on  simulation technique to investigate the mentioned results about order statistics and copulas. The study concentrates on two well known Archimedean Gumbel and Frank families in the case tha...

It is well known that quadrant dependent (QD) random variables are also quadrant dependent in expectation (QDE). Recent literature has offered examples rigorously establishing the fact that there are QDE random variables which are not QD. The examples are based on convex combinations of specially chosen QD copulas: one negatively QD and another positively QD. In this paper we establish general ...

Several extensions of the family (bivariate) Eyraud-Farlie-Gumbel-Morgenstern copulas (EFGM copulas) are considered. Some them well-known from literature, others have recently been suggested (copulas based on quadratic constructions, some forms convexity, and polynomial copulas). For each these we analyze which properties EFGM preserved (or even improved) (partly) lost. Such can be structural (...