ar X iv : 1 10 8 . 09 20 v 2 [ m at h . PR ] 4 A ug 2 01 1 THE MULTIVARIATE PIECING - TOGETHER APPROACH REVISITED
نویسنده
چکیده
The univariate Piecing-Together approach (PT) fits a univariate generalized Pareto distribution (GPD) to the upper tail of a given distribution function (df) in a continuous manner. A multivariate extension was established by Aulbach et al. (2011a): The upper tail of a given copula C was cut off and substituted by the upper tail of a multivariate GPD-copula in a continuous manner. The result is again a copula. The other step consists of the transformation of each margin of this new copula by a given univariate df. This provides, altogether, a multivariate df with prescribed margins, whose copula coincides in its central part with C and in its upper tail with a GPDcopula. While in the paper by Aulbach et al. (2011a) it was merely shown that the upper tail of the generated PT copula is, actually, a GPD copula, we achieve in the present paper an exact characterization, yielding further insight into the multivariate PT approach. A variant based on the empirical copula is also added. Our findings enable us to establish a functional PT version as well.
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