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Erschienen in:
01.12.2012 | Abhandlung
Singular mixture copulas
A geometric method of constructing copulas
Erschienen in: Zeitschrift für die gesamte Versicherungswissenschaft | Ausgabe 5/2012
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Abstract
We present a new family of copulas—the Singular Mixture Copulas. We begin with constructing singular copulas whose supports lie on the graphs of two given quantile functions. These copulas are then mixed with respect to a continuous distribution resulting in a nonsingular parametric copula.
The Singular Mixture Copulas we construct have a Lebesgue density and a closed form representation. Moreover, they have positive lower and upper tail dependence. As an application we fit the copulas to flood level data. As the results show Singular Mixture Copulas provide an alternative to elliptical copulas, e.g., Gaussian and t-copulas, in modeling strongly dependent random variables.