A note on upper-patched generators for Archimedean copulas

Abstract : The class of multivariate Archimedean copulas is defined by using a real-valued function called the generator of the copula. This generator satisfies some properties, including d-monotony. We propose here a new basic transformation of this generator, preserving these properties, thus ensuring the validity of the transformed generator and inducing a proper valid copula. This transformation acts only on a specific portion of the generator, it allows both the non-reduction of the likelihood on a given dataset, and the choice of the upper tail dependence coefficient of the transformed copula. Numerical illustrations show the utility of this construction, which can improve the fit of a given copula both on its central part and its tail.
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Elena Di Bernardino, Didier Rullière. A note on upper-patched generators for Archimedean copulas. ESAIM: Probability and Statistics, EDP Sciences, 2017, ⟨https://doi.org/10.1051/ps/2017003⟩. ⟨10.1051/ps/2017003⟩. ⟨hal-01347869v2⟩

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