  In this paper, we propose a novel approach for estimating Archimedean copula
generators in a conditional setting, incorporating endogenous variables. Our
method allows for the evaluation of the impact of the different levels of
covariates on both the strength and shape of dependence by directly estimating
the generator function rather than the copula itself. As such, we contribute to
relaxing the simplifying assumption inherent in traditional copula modeling. We
demonstrate the effectiveness of our methodology through applications in two
diverse settings: a diabetic retinopathy study and a claims reserving analysis.
In both cases, we show how considering the influence of covariates enables a
more accurate capture of the underlying dependence structure in the data, thus
enhancing the applicability of copula models, particularly in actuarial
contexts.
