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Aggregation Functions in Theory and in Practise pp 59–65Cite as

Copulas and Self-affine Functions

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 228))

Abstract

We characterize self-affine functions whose graphs are the support of a copula using the fact that the functions defined on the unit interval whose graphs support a copula are those that are Lebesgue-measure-preserving. This result allows the computation of the Hausdorff, packing, and box-counting dimensions. The discussion is applied to a classic example such as the Peano curve.

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Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Almería, Almeria, Spain

    Enrique de Amo

  2. Departamento de Análisis Matemático, Universidad de Granada, Granada, Spain

    Manuel Díaz Carrillo

  3. Grupo de Investigación de Análisis Matemático, Universidad de Almería, Almeria, Spain

    Juan Fernández Sánchez

Authors
  1. Enrique de Amo
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  2. Manuel Díaz Carrillo
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  3. Juan Fernández Sánchez
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Corresponding author

Correspondence to Enrique de Amo .

Editor information

Editors and Affiliations

  1. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Humberto Bustince

  2. Department of Automatica y Computacion, Universidad Publica de Navarra, Pamplona, Spain

    Javier Fernandez

  3. Department of Mathematics and, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  4. Department of Computer Science, Universidad de Alcalá de Henares, Madrid, Spain

    Tomasa Calvo

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de Amo, E., Carrillo, M.D., Sánchez, J.F. (2013). Copulas and Self-affine Functions. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds) Aggregation Functions in Theory and in Practise. Advances in Intelligent Systems and Computing, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39165-1_9

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  • DOI: https://doi.org/10.1007/978-3-642-39165-1_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39164-4

  • Online ISBN: 978-3-642-39165-1

  • eBook Packages: EngineeringEngineering (R0)

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