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From Multivariate Skewed Distributions to Copulas

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Combinatorial Matrix Theory and Generalized Inverses of Matrices

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.

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Acknowledgements

The authors are thankful for financial support through ERF grant 9127 and by targeted financing project SF0180015s12.

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Authors and Affiliations

  1. Institute of Mathematical Statistics, University of Tartu, J. Liivi 2, Tartu, 50409, Estonia

    Tõnu Kollo & Anne Selart

  2. Department of Public Health, University of Tartu, Ravila 19, Tartu, 50411, Estonia

    Helle Visk

Authors
  1. Tõnu Kollo
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  2. Anne Selart
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  3. Helle Visk
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Corresponding author

Correspondence to Tõnu Kollo .

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Editors and Affiliations

  1. Indian Statistical Institute, S.J.S. Sansanwal Marg 7, New Delhi, 110016, India

    Ravindra B. Bapat

  2. Hamilton Institute, National University of Ireland, Kilkenny, Maynooth, Co. Kildar, Kilkenny, Ireland

    Steve J. Kirkland

  3. Department of Statistics, Manipal University, manipal.edu, Manipal, 576104, Karnataka, India

    K. Manjunatha Prasad

  4. , School of Information Sciences, University of Tampere, Kalevantie 4,, Tampere, 33014, Finland

    Simo Puntanen

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Kollo, T., Selart, A., Visk, H. (2013). From Multivariate Skewed Distributions to Copulas. In: Bapat, R., Kirkland, S., Prasad, K., Puntanen, S. (eds) Combinatorial Matrix Theory and Generalized Inverses of Matrices. Springer, India. https://doi.org/10.1007/978-81-322-1053-5_6

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