Geodesic
A note on upper-patched generators for Archimedean copulas
Di Bernardino, Elena1  ; Rullière, Didier2 
1 Elena Di Bernardino, CNAM, Paris, EA4629, Département IMATH, 292 rue Saint-Martin, Paris cedex 03, France.
2 Didier Rullière, Université de Lyon, Université Lyon 1, ISFA, Laboratoire SAF, 50 avenue Tony Garnier, 69366 Lyon, France.
ESAIM: Probability and Statistics, Tome 21 (2017), pp. 183-200

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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-monotonicity. 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.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2017003
Classification : 62H20, 62E20, 60E05, 62H05
Keywords: Archimedean copulas, transformations, distortions, tail dependence coefficients, likelihood

Di Bernardino, Elena 1 ; Rullière, Didier 2

1 Elena Di Bernardino, CNAM, Paris, EA4629, Département IMATH, 292 rue Saint-Martin, Paris cedex 03, France.
2 Didier Rullière, Université de Lyon, Université Lyon 1, ISFA, Laboratoire SAF, 50 avenue Tony Garnier, 69366 Lyon, France. 
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     title = {A note on upper-patched generators for {Archimedean} copulas},
     journal = {ESAIM: Probability and Statistics},
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     publisher = {EDP-Sciences},
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Di Bernardino, Elena; Rullière, Didier. A note on upper-patched generators for Archimedean copulas. ESAIM: Probability and Statistics, Tome 21 (2017), pp. 183-200. doi: 10.1051/ps/2017003

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