Multivariate Archimedean copulas, d-monotone functions and ℓ1-norm symmetric distributions

@article{McNeil2009MultivariateAC,
  title={Multivariate Archimedean copulas, d-monotone functions and ℓ1-norm symmetric distributions},
  author={A. McNeil and Johanna Nevslehov'a},
  journal={Annals of Statistics},
  year={2009},
  volume={37},
  pages={3059-3097}
}
  • A. McNeil, Johanna Nevslehov'a
  • Published 2009
  • Mathematics
  • Annals of Statistics
  • It is shown that a necessary and sufficient condition for an Archimedean copula generator to generate a d-dimensional copula is that the generator is a d-monotone function. The class of d-dimensional Archimedean copulas is shown to coincide with the class of survival copulas of d-dimensional l 1 ; -norm symmetric distributions that place no point mass at the origin. The d-monotone Archimedean copula generators may be characterized using a little-known integral transform of Williamson [Duke Math… CONTINUE READING

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