4 Marshall-Olkin copulas
In this section we discuss a class of copulas called Marshall-Olkin copulas. To be able to derive these copulas and present explicit expressions for rank correlation and tail dependence coefficients without tedious calculations, we begin with bivariate Marshall-Olkin copulas. We then continue with the general n-dimensional case and suggest applications of Marshall-Olkin copulas to the modelling of dependent risks. For further details about
Marshall-Olkin distributions we refer to Marshall and Olkin (1967). Similar ideas are contained in Muliere and Scarsini (1987).
4.1 Bivariate Marshall–Olkin copulas
Consider a two-component system where the components are subject to shocks, which are fatal to one or both components. Let ...
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