Dependence modelling with regular vine copula models: A case-study for car crash simulation data

Summary: The analysis of car crash output parameters such as firewall intrusion points assist the overall engineering process. Such data are nowadays collected from many numerical simulations and it is not possible for the engineer to analyse this growing amount of data by hand. Therefore, data mining and statistical methods are needed. Here, we propose to use the flexible class of regular vine (R-vine) copulas for modelling the dependence between such output variables. R-vine copulas are multivariate copulas constructed hierarchically from bivariate copulas as building blocks. We introduce the concept of such constructions and their graphical tree representation. Applied to simulated frontal crash data of a Ford Taurus such graphs help us to illustrate the dependence structure among different firewall intrusion locations. The big advantage of R-vines compared with standard approaches such as the multivariate normal distribution or the multivariate Gaussian copula is the ability to model asymmetries and dependence in the tails. Our application demonstrates the strong potential of R-vines in the engineering context and opens further application areas.