# Multivariate Unified Skew-t Distributions And Their Properties

arXiv: https://arxiv.org/abs/2311.18294 · HTML: https://mlsanity.com/paper/2311.18294/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2023.

## Built on by (most cited first, 1 of 1)

- [A Generalized Unified Skew-Normal Process with Neural Bayes Inference](https://mlsanity.com/paper/2411.17400/) (2024)

## Abstract (arXiv)

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.