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Multivariate unified skew-t distributions and their properties

Author

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  • Wang, Kesen
  • Karling, Maicon J.
  • Arellano-Valle, Reinaldo B.
  • Genton, Marc G.

Abstract

The unified skew-t (SUT) is a flexible parametric multivariate distribution that accounts for skewness and heavy tails in the data. A few of its properties can be found scattered in the literature or in a parameterization that does not follow the original one for unified skew-normal (SUN) distributions, yet a systematic study is lacking. In this work, explicit properties of the multivariate SUT distribution are presented, such as its stochastic representations, moments, SUN-scale mixture representation, linear transformation, additivity, marginal distribution, canonical form, quadratic form, conditional distribution, change of latent dimensions, Mardia measures of multivariate skewness and kurtosis, and non-identifiability issue. These results are given in a parameterization that reduces to the original SUN distribution as a sub-model, hence facilitating the use of the SUT for applications. Several models based on the SUT distribution are provided for illustration.

Suggested Citation

  • Wang, Kesen & Karling, Maicon J. & Arellano-Valle, Reinaldo B. & Genton, Marc G., 2024. "Multivariate unified skew-t distributions and their properties," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    • Handle: RePEc:eee:jmvana:v:203:y:2024:i:c:s0047259x24000290
    DOI: 10.1016/j.jmva.2024.105322
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