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Joint Distributions of Random Sets and Their Relation to Copulas

  • Conference paper
Modeling Dependence in Econometrics

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 251))

Abstract

Random sets are set-valued random variables. They have been applied in various fields like stochastic geometry, statistics, economics, engineering or computer science, and are often used for modeling uncertainty. This paper is concerned with joint distributions of random sets. Generalizations of the Choquet theorem are presented which state that the joint distribution of random sets can be characterized by multivariate analogues of capacity functionals. Furthermore, it is shown how copulas can be used to describe the relation between a joint distribution of random sets and their marginal distribution.

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Author information

Authors and Affiliations

  1. Salzburger Strasse 14, 6300, Woergl, Austria

    Bernhard Schmelzer

Authors
  1. Bernhard Schmelzer
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Correspondence to Bernhard Schmelzer .

Editor information

Editors and Affiliations

  1. APAN Advanced Institute of Science and Technology, Ishikawa, Japan

    Van-Nam Huynh

  2. Department of Computer Science, University of Texas at El Paso, El Paso, Texas, USA

    Vladik Kreinovich

  3. Faculty of Economics, Chiangmai University, Chiangmai, Thailand

    Songsak Sriboonchitta

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© 2014 Springer International Publishing Switzerland

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Schmelzer, B. (2014). Joint Distributions of Random Sets and Their Relation to Copulas. In: Huynh, VN., Kreinovich, V., Sriboonchitta, S. (eds) Modeling Dependence in Econometrics. Advances in Intelligent Systems and Computing, vol 251. Springer, Cham. https://doi.org/10.1007/978-3-319-03395-2_10

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  • DOI: https://doi.org/10.1007/978-3-319-03395-2_10

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03394-5

  • Online ISBN: 978-3-319-03395-2

  • eBook Packages: EngineeringEngineering (R0)

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