Some multivariate imprecise shock model copulas. (English) Zbl 1522.62029
Summary: Although bivariate imprecise copulas have recently attracted substantial attention, the multivariate case seems still to be open. So, it is natural to test it first on shock model induced copulas, a family which might be the most useful in various applications. We investigate a model in which some of the shocks are assumed imprecise and develop the corresponding set of copulas. In the Marshall’s case we get a coherent set of distributions and a coherent set of copulas, where the bounds are naturally corresponding to each other. The situation in the other two groups of multivariate imprecise shock model induced copulas, i.e., the maxmin and the reflected maxmin (RMM) copulas, is substantially more involved, but we are still able to exhibit their properties. These are the main results of the paper that serves as the first step into a theory that should develop in this direction. Also, the theory of imprecise RMM copulas seems to be new even in the bivariate case. It turns out that all imprecise copulas under consideration are coherent.
MSC:
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
Keywords:
imprecise probability; shock model; Marshall’s copula; maxmin copula; reflected maxmin copulaSoftware:
CopulaModelReferences:
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