We present a constructive and self-contained approach to data driven infinite partition-of-unity copulas that were recently introduced in the literature. In particular, we consider negative binomial and Poisson copulas and present a solution to the problem of fitting such copulas to highly asymmetric data in arbitrary dimensions.
In this paper we consider the problem of estimating the intensity of a spatial homogeneous Poisson process if a part of the observations (quadrat counts) is censored. The actual problem has occurred during a court case when one of the authors was a referee for the defense.
We construct new multivariate copulas on the basis of a generalized infinite partition-of-unity approach. This approach allows, in contrast to finite partition-of-unity copulas, for tail-dependence as well as for asymmetry. A possibility of fitting such copulas to real data from quantitative risk management is also pointed out.
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