Copula-based multivariate input modeling

In this survey, we review the copula-based input models that are well suited to provide multivariate input-modeling support for stochastic simulations with dependent inputs. Specifically, we consider the situation in which the dependence between pairs of simulation input random variables is measured by tail dependence (i.e., the amount of dependence in the tails of a bivariate distribution) and review the techniques to construct copula-based input models representing positive tail dependencies. We complement the review with the parameter estimation from multivariate input data and the random-vector generation from the estimated input model with the purpose of driving the simulation.

► Considers tail dependence to measure dependence between inputs.
► Reviews various techniques to construct multivariate copula-based input models.
► Provides data-fitting and sampling algorithms with goodness-of-fit tests.
► Reviews various applications of copula theory with emphasis on tail dependence.