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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

Cite Score 2018: 0.85

SCImago Journal Rank (SJR) 2018: 0.354
Source Normalized Impact per Paper (SNIP) 2018: 0.604

Mathematical Citation Quotient (MCQ) 2018: 0.36

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Volume 30, Issue 1


Properties of hierarchical Archimedean copulas

Ostap Okhrin
  • Insitute for Statistics and Econometries, Humboldt Universität zu Berlin, Berlin, Deutschland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Yarema Okhrin / Wolfgang Schmid
Published Online: 2013-03-06 | DOI: https://doi.org/10.1524/strm.2013.1071


In this paper we analyse the properties of hierarchical Archimedean copulas. This class is a generalisation of the Archimedean copulas and allows for general non-exchangeable dependency structures. We show that the structure of the copula can be uniquely recovered from all bivariate margins. We derive the distribution of the copula values, which is particularly useful for tests and constructing confidence intervals. Furthermore, we analyse dependence orderings, multivariate dependence measures, and extreme value copulas. We pay special attention to the tail dependencies and derive several tail dependence indices for general hierarchical Archimedean copulas.

Keywords: copula; multivariate distribution; Archimedean copula; stochastic ordering; hierarchical copula

About the article

* Correspondence address: Universität Augsburg, Lehrstuhl für Statistik, Universitätsstr. 16, 86159 Augsburg, Deutschland,

Published Online: 2013-03-06

Published in Print: 2013-03-01

Citation Information: Statistics & Risk Modeling with Applications in Finance and Insurance, Volume 30, Issue 1, Pages 21–54, ISSN (Print) 2193-1402, DOI: https://doi.org/10.1524/strm.2013.1071.

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