We discuss a new construction method for obtaining additive generators of Archimedeancopulas proposed by McNeil and Neslehova [8], the so-called Williamson n-transform,and illustrate it by several examples. We show that due to the equivalence of convergencesof positive distance functions, additive generators and copulas, we may approximateany n-dimensional Archimedean copula by an Archimedean copula generated bya transformation of a weighted sum of Dirac functions concentrated in certain suitablepoints. Specically, in two-dimensional case this means that any Archimedean copulacan be approximated by a piece-wise linear Archimedean copula, moreover the approximationof the generator by linear splines circumvents the problem with the non-existenceof explicit inverse.
@article{494,
title = {Convergence of Linear Approximation of Archimedean Generator from Williamson's Transform in Examples},
journal = {Tatra Mountains Mathematical Publications},
volume = {70},
year = {2018},
language = {EN},
url = {http://dml.mathdoc.fr/item/494}
}
Bacigál, Tomáš; Ždímalová, Mária. Convergence of Linear Approximation of Archimedean Generator from Williamson's Transform in Examples. Tatra Mountains Mathematical Publications, Tome 70 (2018) . http://gdmltest.u-ga.fr/item/494/