Liouville copulas, which were introduced in [27], are asymmetric generalizations of the ubiquitous Archimedean copula class. They are the dependence structures of scale mixtures of Dirichlet distributions, also called Liouville distributions. In this paper, the limiting extreme-value copulas of Liouville copulas and of their survival counterparts are derived. The limiting max-stable models, ter...

Abstract. In this paper we are concentrated on a problem of linear chanceconstrained programming where the constraint matrix is considered random with a known distribution of the matrix rows. The rows are not considered to be independent; instead, we make use of the copula notion to describe the dependence of the matrix rows. In particular, the distribution of the rows is driven by so-called Ar...

Understanding and quantifying dependence is at the core of all modelling efforts in financial econometrics. The linear correlation coefficient, which is the far most used measure to test dependence in the financial community and also elsewhere, is only a measure of linear dependence. This means that it is a meaningful measure of dependence if asset returns are well represented by an elliptical ...

In recent years analyses of dependence structures using copulas have become more popular than the standard correlation analysis. Starting from Aas, Czado, Frigessi, and Bakken (2009) regular vine pair-copula constructions (PCCs) are considered the most flexible class of multivariate copulas. PCCs are involved objects but (conditional) independence present in data can simplify and reduce them si...

Implicit copulas are the most common copula choice for modeling dependence in high dimensions. This broad class of is introduced and surveyed, including elliptical copulas, skew t factor time series regression copulas. The auxiliary representation implicit outlined, how this makes them both scalable tractable statistical modeling. Issues such as parameter identification, extended likelihoods di...

We propose a model able to describe the Interspike Intervals of two or more neurons subject to common inputs from the network. The single neuron dynamic is described through a classical Leaky Integrate and Fire model, but the model also catches the joint behavior of two neurons resorting to the use of copulas. Copulas are mathematical objects largely used to describe dependencies laws. Synchron...

In this work we summarize some of recent and classical results on the role played by copulas in the analysis of chaotic processes and univariate time series. We review some aspects of the copulas related to chaotic process, its properties and applications. We also present a review on classical and modern approaches to understand the relationship among random variables in Markov processes as wel...

In this review paper we outline some recent contributions to copula theory. Several new author's investigations are presented brie°y, namely: order statistics copula, copulas with given multivariate marginals, copula representation via a local dependence measure and applications of extreme value copulas. Key-words: Copula; Dependence measures; Extremes; Kendall distribution; Local dependence; M...