Constructing symmetric generalized FGM copulas by means of certain univariate distributions

Matthias J. Fischer and Ingo Klein

No 61/2004, Discussion Papers from Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics

Abstract: In this paper we focus on symmetric generalized Fairlie-Gumbel-Morgenstern (or symmetric Sarmanov) copulas which are characterized by means of so-called generator functions. In particular, we introduce a class of generator functions which is based on univariate distributions with certain properties. Some of the generator functions from the literature are recovered. Moreover two new generators are suggested, implying two new copulas. Finally, the opposite way around, it is exemplarily shown how to calculate the univariate distribution which belongs to a given copula generator function.

Date: 2004
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