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arXiv · 2311.18294

Multivariate Unified Skew-t Distributions And Their Properties

Kesen Wang·Maicon J. Karling·Reinaldo B. Arellano-Valle·Marc G. Genton
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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 parametrization 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.

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Kesen Wang, Maicon J. Karling, Reinaldo B. Arellano-Valle, Marc G. Genton. 2023-11-30. Multivariate Unified Skew-t Distributions And Their Properties. https://arxiv.org/abs/2311.18294

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