The goal of this presentation is to introduce new families of multivariate copulas, extending the chi-square copulas, the Fisher copula, and squared copulas. The new families are constructed from existing copulas by first transforming their margins to standard Gaussian distributions, then transforming these variables into non-central chi-square variables with one degree of freedom, and finally by considering the copula associated with these new variables. It is shown that by varying the non-centrality parameters, one can model non-monotonic dependence, and when one or many non-centrality parameters are outside a given hyper-rectangle, then the copula is almost the same as the one when these parameters are infinite. For these new families, the tail behavior, the monotonicity of dependence measures such as Kendall’s tau and Spearman’s rho are investigated, and estimation is discussed. Some examples will illustrate the usefulness of these new copula families.
Dr. Nasri is Assistant Professor in Statistics at the Scholl of Public Health of Univesité de Montréal. Her research interests are dependence modelling, time series, and more recently spatial modelling. The main applications targeted by her research projects are related to climate change, public health and infectious diseases modelling. Dr. Nasri is an associate director of the new infectious diseases network OMNI-RÉUNIS.