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Archimedean copulas with applications to VaR estimation. (English) Zbl 1373.60029

Summary: Assuming absolute continuity of marginals, we give the distribution for sums of dependent random variables from some class of Archimedean copulas and the marginal distribution functions of all order statistics. We use conditional independence structure of random variables from this class of Archimedean copulas and Laplace transform. Additionally, we present an application of our results to VaR estimation for sums of data from Archimedean copulas.

MSC:

60E05 Probability distributions: general theory
62G30 Order statistics; empirical distribution functions
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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