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The centred parameterization and related quantities of the skew-t distribution

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  • Arellano-Valle, Reinaldo B.
  • Azzalini, Adelchi

Abstract

The skew-t family, in its univariate and multivariate versions, is a parametric family of probability distributions which is currently under intense investigation because of several appealing properties. The present paper addresses the question of the choice of its parameterization, and more generally of the selection of quantities of interest associated to this distribution.

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  • Arellano-Valle, Reinaldo B. & Azzalini, Adelchi, 2013. "The centred parameterization and related quantities of the skew-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 73-90.
    • Handle: RePEc:eee:jmvana:v:113:y:2013:i:c:p:73-90
    DOI: 10.1016/j.jmva.2011.05.016
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    References listed on IDEAS

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    3. Adelchi Azzalini, 2005. "The Skew‐normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
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    5. Kim, Hyoung-Moon & Mallick, Bani K., 2003. "Moments of random vectors with skew t distribution and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 417-423, July.
    6. Arellano-Valle, Reinaldo B. & Azzalini, Adelchi, 2008. "The centred parametrization for the multivariate skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1362-1382, August.
    7. Reinaldo B. Arellano-Valle, 2010. "On the information matrix of the multivariate skew-t model," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 371-386.
    8. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    9. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    10. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    11. Monica Chiogna, 2005. "A note on the asymptotic distribution of the maximum likelihood estimator for the scalar skew-normal distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(3), pages 331-341, December.
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    2. Wang, Sheng & Zimmerman, Dale L. & Breheny, Patrick, 2020. "Sparsity-regularized skewness estimation for the multivariate skew normal and multivariate skew t distributions," Journal of Multivariate Analysis, Elsevier, vol. 179(C).

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