Some algebraic properties of Archimedean copula functions and their applications in the statistical estimation of the survival function

In this paper we study some algebraic properties of Archimedean copulas and simple smoothed estimator of distribution function under random right censored observations in the presence of covariate. Where the dependence between a life time and a censoring variable may expressed by a given Archimedean copula. We prove an almost sure asymptotic representation which provides a key tool for obtaining weak convergence result for estimator.