New results on perturbation-based copulas

Abstract A prominent example of a perturbation the bivariate product copula (which characterizes stochastic independence) is parametric family Eyraud-Farlie-Gumbel-Morgenstern copulas which allows small dependencies to be modeled. We introduce and discuss several perturbations, some them perturbing copula, while others perturb general copulas. particularly interesting case based on two functions in one variable where we highlight special phenomena, e.g., extremal perturbed The constructions perturbations this paper include three different types ordinal sums as well flippings survival copula. Some particular relationships Markov dependence parameters for considered here are also given.