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.

翻译：统一偏t（SUT）分布是一种灵活的参数化多元分布，能够刻画数据中的偏态和厚尾特性。其部分性质虽散见于文献中，或存在于未遵循统一偏正态（SUN）分布原始参数化的其他参数化形式中，但尚缺乏系统性研究。本文系统阐述了多元SUT分布的显式性质，包括其随机表示、矩、SUN尺度混合表示、线性变换、可加性、边缘分布、规范形式、二次型、条件分布、隐维度变换、多元偏度与峰度的Mardia度量以及非可识别性问题。所有结论均基于一种能退化为原始SUN分布（作为子模型）的参数化形式，从而便于SUT分布的实际应用。文中还提供了若干基于SUT分布的模型作为示例。