2023/11/30 by Kesen Wang, Maicon J. Karling, Wang, Kesen +5
Agricultural and Biological Sciences · Mathematics · #Agricultural Economics and Practices #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2311.18294
openalex publication_date 2023/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.