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We use the conditional distribution and conditional expectation of one random variable given the other one being large to capture the strength of dependence in the tails of a bivariate random vector. We study the tail behavior of the boundary conditional cumulative distribution function (cdf) and two forms of conditional tail expectation (CTE) for various… (More)

Tail dependence and conditional tail dependence functions describe, respectively, the tail probabilities and conditional tail probabilities of a copula at various relative scales. The properties as well as the interplay of these two functions are established based upon their homogeneous structures. The extremal dependence of a copula, as described by its… (More)

In order to study copula families that have different tail patterns and tail asymmetry than mul-tivariate 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… (More)