Abstract
We show several interesting examples of connection between distribution of a positively valued random variable and an Archimedean copula through Williamson’s transformation (and Laplace transform), especially when arranged in a sequence. Naturally, there appears a question: how can we use statistical properties of distance functions to draw statistical properties of copulas, and vice versa? This question is formulated in two open problems.
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The work on this paper was supported by grant APVV-14-0013.
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Bacigál, T. (2018). On Some Applications of Williamson’s Transform in Copula Theory. In: Torra, V., Mesiar, R., Baets, B. (eds) Aggregation Functions in Theory and in Practice. AGOP 2017. Advances in Intelligent Systems and Computing, vol 581. Springer, Cham. https://doi.org/10.1007/978-3-319-59306-7_3
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DOI: https://doi.org/10.1007/978-3-319-59306-7_3
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