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Title: Frechet-Hoeffding copula bounds for circular data Authors:  Hiroaki Ogata - Tokyo Metropolitan University (Japan) [presenting]
Abstract: A simple extension of the Frechet-Hoeffding copula bounds for circular data is proposed. Copulas are a powerful tool for describing the dependency of random variables. In two dimensions, Frechet-Hoeffding upper (lower) bound indicates the perfect positive (negative) dependence between two random variables. However, for circular random variables, the usual concept of dependency is not accepted, because of their periodicity. We redefine the Frechet-Hoeffding bounds and consider modified Frechet and Mardia families of copulas for modelling the dependency of two circular random variables. Simulation studies are also given to show the behavior of the model.