Multivariate distributions from mixtures of max-infinitely divisible distributions
Journal of Multivariate Analysis
Multivariate survival functions with a min-stable property
Journal of Multivariate Analysis
Probability Density Decomposition for Conditionally Dependent Random Variables Modeled by Vines
Annals of Mathematics and Artificial Intelligence
Tails of multivariate Archimedean copulas
Journal of Multivariate Analysis
Tail dependence functions and vine copulas
Journal of Multivariate Analysis
Scale mixtures of Kotz-Dirichlet distributions
Journal of Multivariate Analysis
Extremal dependence of copulas: A tail density approach
Journal of Multivariate Analysis
Factor copula models for multivariate data
Journal of Multivariate Analysis
Geometric interpretation of the residual dependence coefficient
Journal of Multivariate Analysis
Strength of tail dependence based on conditional tail expectation
Journal of Multivariate Analysis
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In order to study copula families that have tail patterns and tail asymmetry different from 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 Archimedean copula, we relate the tail heaviness of a positive random variable to the tail behavior of the Archimedean copula constructed from the Laplace transform of the random variable, and extend the results of Charpentier and Segers [7] [A. Charpentier, J. Segers, Tails of multivariate Archimedean copulas, Journal of Multivariate Analysis 100 (7) (2009) 1521-1537] for upper tails of Archimedean copulas. In addition, a new one-parameter Archimedean copula family based on the Laplace transform of the inverse Gamma distribution is proposed; it possesses patterns of upper and lower tails not seen in commonly used copula families. Finally, tail orders are studied for copulas constructed from mixtures of max-infinitely divisible copulas.