We propose a new approach for estimation of joint densities for continuous observations using latent tree models for copulas, joint distributions with uniform U (0, 1) marginals. Latent tree copulas combine the advantages of the parametrization of the joint density using only bivariate distributions with the ability to approximate complex dependencies with the help of latent variables. The prop...

We review and extend the now considerable literature on Lévy copulas. First, we focus on Monte Carlo methods and present a new robust algorithm for the simulation of multidimensional Lévy processes with dependence given by a Lévy copula. Next, we review statistical estimation techniques in a parametric and a non-parametric setting. Finally, we discuss the interplay between Lévy copulas and mult...

Quasi-homogeneity of copulas is introduced and studied. Quasi-homogeneous copulas are characterized by the convexity and strict monotonicity of their diagonal sections. As a by-product, a new construction method for copulas when only their diagonal section is known is given.

Copulas offer a useful tool in modelling the dependence among random variables. In the literature, most of the existing copulas are symmetric while data collected from the real world may exhibit asymmetric nature. This necessitates developing asymmetric copulas that can model such data. In the meantime, existing methods of modelling two-dimensional reliability data are not able to capture the t...

A statistical interpretation of recently introduced discrete copulas is given, and the composition of discrete copulas is clarified.

2 Copulas: first definitions and examples 3 2.1 Sklar’s theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Copula densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Conditional distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Bounds of copulas . . . . . . . . . . . . . . . . . . . . . . ...

Abstract Two-dimensional distribution function g ( x, y ) defined in [0, 1] 2 is called copula, if 1) = x and (1, )= for every . Similarly, s -dimensional copula a 1 , ,..., such that k face g ( 1 , … x i </m...

Considering two different metrics on the space of two-dimensional copulas C we prove some Baire category results for important subclasses of copulas, including the families of exchangeable, associative, and Archimedean copulas. From the point of view of Baire categories, with respect to the uniform metric d∞, a typical copula is not symmetric and a typical symmetric copula is not associative, w...

Copulas recently emerged in many data analysis and knowledge discovery tasks as a flexible tool for modeling complex multivariate distributions. The paper presents a method for estimating copulas from one of the most popular classes of copulas, namely hierarchical Archimedean copulas. The method is based on the close relationship of the copula structure and the values of Kendall’s tau computed ...

Although the copula literature has many instances of bivariate copulas, once more than two variates are correl ated, the choice of copulas often comes down to selection of the degrees-of-freedom parameter in the t-copula. In search for a wider selection of multivariate copulas we review a generalization of the t-copula and some copulas defined by Harry Joe. Generalizing the t-copula gives more ...