Estimation procedures for exchangeable Marshall copulas with hydrological application

  • Fabrizio DuranteEmail author
  • Ostap Okhrin
Original Paper


Complex phenomena in environmental sciences can be conveniently represented by several inter-dependent random variables. In order to describe such situations, copula-based models have been studied during the last year. In this paper, we consider a novel family of bivariate copulas, called exchangeable Marshall copulas. Such copulas describe both positive and (upper) tail association between random variables. Specifically, inference procedures for the family of exchangeable Marshall copulas are introduced, based on the estimation of their (univariate) generator. Moreover, the performance of the proposed methodologies is shown in a simulation study. Finally, an illustration describes how the proposed procedures can be useful in a hydrological application.


Copula Kendall distribution Marshall–Olkin distribution Non-parametric estimation Risk management 



We would like to thank the Reviewers for the careful reading and useful suggestions that improved the previous version of the manuscript. The first author acknowledges the support of Free University of Bozen-Bolzano via the project MODEX. The financial support from the Deutsche Forschungsgemeinschaft via SFB 649 “Ökonomisches Risiko”, Humboldt-Universität zu Berlin is gratefully acknowledged by the second author.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Economics and ManagementFree University of Bozen-BolzanoBolzanoItaly
  2. 2.Ladislaus von Bortkiewitcz Chair of Statistics, Center of Applied Statistics and Economics (C.A.S.E.)Humboldt-Universität zu BerlinBerlinGermany

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