Practical approach to dependence modelling using copulas

Abstract

Modelling the stochastic dependence between random inputs of a system is of uttermost importance for a sensible evaluation of its reliability. Most of the time, this modelling is made using some linear correlation coefficients. The current paper underlines the potential pitfalls of such an approach and gives a short introduction to the concept of copula, which appears to be the exact concept of stochastic dependence from a theoretical point of view. From a practical point of view, the identification of the copula of a multi-dimensional random vector can be challenging. After a short presentation of the concept of measure of association, the current paper introduces the new concept of dependence information as a multi-scalar synthesis of the copula. Thanks to several numerical simulations, it proposes first practical rules to select a copula for the dependence modelling, based on specific dependence information and the expected reliability level of the system under study.