Copula bounds for circular data

06/21/2022

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by   Hiroaki Ogata, et al.

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We propose the extension of Fréchet-Hoeffding copula bounds for circular data. The copula is a powerful tool for describing the dependency of random variables. In two dimensions, the Fréchet-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. In this work, we redefine Fréchet-Hoeffding bounds and consider modified Fréchet and Mardia families of copulas for modelling the dependency of two circular random variables. Simulation studies are also given to demonstrate the behavior of the model.