Multivariate unified skew-t distributions and their properties

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

Journal of Multivariate Analysis, 2024, vol. 203, issue C

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.

Keywords: Heavy tail; Latent variable; Selection distribution; Skewness; Unified skew-normal distribution; Unified skew-t distribution (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.jmva.2024.105322

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