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Multivariate copulas with given values at two arbitrary points

Author

Listed:
  • Erich Peter Klement

    (Johannes Kepler University Linz)

  • Damjana Kokol Bukovšek

    (University of Ljubljana)

  • Matjaž Omladič

    (Institute of Mathematics, Physics and Mechanics)

  • Susanne Saminger-Platz

    (Johannes Kepler University Linz)

  • Nik Stopar

    (University of Ljubljana)

Abstract

Copulas are functions that link an n-dimensional distribution function with its one-dimensional margins. In this contribution we show how n-variate copulas with given values at two arbitrary points can be constructed. Thereby, we also answer a so far open question whether lower and upper bounds for n-variate copulas with given value at a single arbitrary point are achieved. We also introduce and discuss the concept of an $$\mathbf{F}$$ F -copula which is needed for proving our results.

Suggested Citation

  • Erich Peter Klement & Damjana Kokol Bukovšek & Matjaž Omladič & Susanne Saminger-Platz & Nik Stopar, 2023. "Multivariate copulas with given values at two arbitrary points," Statistical Papers, Springer, vol. 64(6), pages 2015-2055, December.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:6:d:10.1007_s00362-022-01362-4
    DOI: 10.1007/s00362-022-01362-4
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