Convergence of a sequence of bivariate Archimedean copulas to another Archimedean copula or to the comonotone copula is shown to be equivalent with convergence of the corresponding sequence of Kendall distribution functions. No extra differentiability conditions on the generators are needed. r 2007 Elsevier B.V. All rights reserved.

A class of bivariate integer-valued time series models was constructed via copula theory. Each follows a Markov chain with the serial dependence captured using copula-based transition probabilities from Poisson and zero-inflated (ZIP) margins. The theory also used again to capture between two either Gaussian or “t-copula” functions. Such method provides flexible structure that allows for positi...

In order to study copula families that have different tail patterns and tail asymmetry than multivariate Gaussian and t copulas, we introduce the concepts of tail order and tail order functions. These provide an integrated way to study both tail dependence and intermediate tail dependence. Some fundamental properties of tail order and tail order functions are obtained. For the multivariate Arch...

Estimating the probability of extreme temperature events is difficult because of limited records across time and the need to extrapolate the distributions of these events, as opposed to just the mean, to locations where observations are not available. Another related issue is the need to characterize the uncertainty in the estimated probability of extreme events at different locations. Although...

Copula-based models provide a great deal of flexibility in modelling multivariate distributions, allowing for the specifications marginal distributions separately from dependence structure (copula) that links them to form joint distribution. Choosing class copula is not trivial task and its misspecification can lead wrong conclusions. We introduce novel grid-uniform functions, which dense space...

A notion of higher order tail densities for copulas is introduced using multivariate regular variation of copula densities, and densities of multivariate extremes with various margins can then be studied in a unified fashion. We show that the tail of a multivariate density can be decomposed into the tail density of the underlying copula, coupled with marginal tail transforms of the three types:...

A continuous random vector (X,Y) uniquely determines a copula C : [0,1]2 → [0,1] such that when the distribution functions of X and Y are properly composed into C , the joint distribution function of (X,Y) results. A copula is said to be D4-invariant if its mass distribution is invariant with respect to the symmetries of the unit square. A D4-invariant copula leads naturally to a family of meas...