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From Multivariate Skewed Distributions to Copulas

In: Combinatorial Matrix Theory and Generalized Inverses of Matrices

Author

Listed:
  • Tõnu Kollo

    (University of Tartu, Institute of Mathematical Statistics)

  • Anne Selart

    (University of Tartu, Institute of Mathematical Statistics)

  • Helle Visk

    (University of Tartu, Department of Public Health)

Abstract

In this paper, a methodology is presented for constructing skewed multivariate copulas to model data with possibly different marginal distributions. Multivariate skew elliptical distributions are transformed into corresponding copulas in the similar way as the Gaussian copula and the multivariate t-copula are constructed. Three-parameter skew elliptical distributions are under consideration. For parameter estimation of the skewed distributions, the method of moments is used. To transform mixed third-order moments into a parameter vector, the star product of matrices is used; for star product and its applications, see, for example, Kollo (J. Multivar. Anal. 99:2328–2338, 2008) or Visk (Commun. Stat. 38:461–470, 2009). Results of the first applications are shortly described and referred to.

Suggested Citation

  • Tõnu Kollo & Anne Selart & Helle Visk, 2013. "From Multivariate Skewed Distributions to Copulas," Springer Books, in: Ravindra B. Bapat & Steve J. Kirkland & K. Manjunatha Prasad & Simo Puntanen (ed.), Combinatorial Matrix Theory and Generalized Inverses of Matrices, edition 127, pages 63-72, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-1053-5_6
    DOI: 10.1007/978-81-322-1053-5_6
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