Multivariate distributions from mixtures of max-infinitely divisible distributions
Journal of Multivariate Analysis
Computational Statistics & Data Analysis
An Introduction to Copulas
Sampling Exponentially Tilted Stable Distributions
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Likelihood inference for Archimedean copulas in high dimensions under known margins
Journal of Multivariate Analysis
Selecting and estimating regular vine copulae and application to financial returns
Computational Statistics & Data Analysis
Nonparametric estimation of the tree structure of a nested Archimedean copula
Computational Statistics & Data Analysis
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Efficient sampling algorithms for both Archimedean and nested Archimedean copulas are presented. First, efficient sampling algorithms for the nested Archimedean families of Ali-Mikhail-Haq, Frank, and Joe are introduced. Second, a general strategy how to build a nested Archimedean copula from a given Archimedean generator is presented. Sampling this copula involves sampling an exponentially tilted stable distribution. A fast rejection algorithm is developed for the more general class of tilted Archimedean generators. It is proven that this algorithm reduces the complexity of the standard rejection algorithm to logarithmic complexity. As an application it is shown that the fast rejection algorithm outperforms existing algorithms for sampling exponentially tilted stable distributions involved, e.g., in nested Clayton copulas. Third, with the additional help of randomization of generator parameters, explicit sampling algorithms for several nested Archimedean copulas based on different Archimedean families are found. Additional results include approximations and some dependence properties, such as Kendall's tau and tail dependence parameters. The presented ideas may also apply in the more general context of sampling distributions given by their Laplace-Stieltjes transforms.