The tail dependence of multivariate distributions is frequently studied via the tool of copulas. This paper develops a general method, which is based on multivariate regular variation, to evaluate the tail dependence of heavy-tailed scale mixtures of multivariate distributions, whose copulas are not explicitly accessible. Tractable formulas for tail dependence parameters are derived, and a suff...

The concept of copulas is normaly used to model the dependence structure between two or more random variables. Random variables are transformed to the unit interval I = [0, 1] by using quasi-inverse transformation. As a result we get a normalised multivariate distribution function called the copula. Copulas uniquely determine the dependence structure of multiple random variables. The aim of the...

Probability distributions are central tools for probabilistic modeling in data mining. In functional data analysis (FDA) they are weakly studied in the general case. In this paper we discuss a probability distribution law for functional data considered as stochastic process. We define first a new kind of stationarity linked t o the Archimedean copulas, and then we build a probability distributi...

These notes provide an introduction to modeling with copulas. Copulas are the mechanism which allows us to isolate the dependency structure in a multivariate distribution. In particular, we can construct any multivariate distribution by separately specifying the marginal distributions and the copula. Copula modeling has played an important role in finance in recent years and has been a source o...

This paper discusses the uses of copulas for modelling multivariate density functions and explains how copula methods can be applied to the study of macroeconomic relationships. It suggests that copulas are well suited to the study of these relationships and can sometimes shed new light on them. It then sets out the main steps of copula methodology and provides an illustrative application to th...

We consider a family of copulas that are invariant under univariate truncation. Such a family has some distinguishing properties: it is generated by means of a univariate function; it can capture non-exchangeable dependence structures; it can be easily simulated. Moreover, such a class presents strong probabilistic similarities with the class of Archimedean copulas from a theoretical and practi...

We study the relationship between multivariate quasi-copulas and measures that they may or may not induce on [0, 1]n . We first study the mass distribution of the pointwise best possible lower bound for the set of n-quasi-copulas for n ≥ 3. As a consequence, we show that not every n-quasi-copula induces a signed measure on [0, 1]n . © 2010 Elsevier B.V. All rights reserved.

The stability of discrete universal integrals based on copulas is discussed and examined, both with respect to the norms L1 (Lipschitz stability) and L∞ (Chebyshev stability). Each of these integrals is shown to be 1-Lipschitz. Exactly the discrete universal integrals based on a copula which is stochastically increasing in its first coordinate turn out to be 1-Chebyshev. A new characterization ...

Our focus is on the joint analysis of longitudinal nonnormal responses and early discontinuation in (pre)-clinical trials. Separate models are fitted to the two series (response and discontinuation) to account for covariate and time effects. The serial dependence and the dependence between response and drop-out are also modeled. This is done using particular dependence functions, called copulas...