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Explicit functional forms for the generator derivatives of well-knownone-parameter Archimedean copulas are derived. These derivatives are essentialfor likelihood inference as they appear in the copula density, conditionaldistribution functions, or the Kendall distribution function. They are alsorequired for several asymmetric extensions of Archimedean copulas such asKhoudraji-transformed Archimedean copulas. Access to the generator derivativesmakes maximum-likelihood estimation for Archimedean copulas feasible in termsof both precision and run time, even in large dimensions. It is shown bysimulation that the root mean squared error is decreasing in the dimension.This decrease is of the same order as the decrease in sample size. Furthermore,confidence intervals for the parameter vector are derived. Moreover, extensionsto multi-parameter Archimedean families are given. All presented methods areimplemented in the open-source R package nacopula and can thus easily beaccessed and studied.

Likelihood inference for Archimedean copulas