Reparameterizing Marshall-Olkin copulas with applications to sampling

It is shown that exchangeable Marshall-Olkin survival copulas coincide with a parametric family of copulas studied in [Mai, Scherer (2009b)]. This observation implies an alternative probabilistic interpretation in many cases and allows the transfer of known results from one family to the other. For instance, using the classical construction of [Marshall, Olkin (1967)], sampling an n-dimensional Marshall-Olkin copula requires 2n-1 exponentially distributed random variables, which is inefficient in large dimensions. Applying the alternative construction, sampling an exchangeable n-dimensional copula boils down to generating n independent exponentially distributed random variables and one path of a certain Lévy subordinator, which is highly efficient in many cases. Furthermore, the alternative model and sampling methodology is generalized to high-dimensional hierarchical copulas. A sampling algorithm for the latter is described in detail and illustrated with an example.      «

It is shown that exchangeable Marshall-Olkin survival copulas coincide with a parametric family of copulas studied in [Mai, Scherer (2009b)]. This observation implies an alternative probabilistic interpretation in many cases and allows the transfer of known results from one family to the other. For instance, using the classical construction of [Marshall, Olkin (1967)], sampling an n-dimensional Marshall-Olkin copula requires 2n-1 exponentially distributed random variables, which is inefficient i...     »