多元统一偏斜t分布及其性质
Multivariate Unified Skew-t Distributions And Their Properties
AI总结：
本文系统研究了多元统一偏斜t（SUT）分布的性质，给出了随机表示、矩、条件分布及偏度峰度测度等结果，并采用兼容原始SUN分布的参数化形式以促进应用。
摘要：
统一偏斜t（SUT）分布是一种灵活的多元参数分布，能够刻画数据中的偏斜性和重尾特征。文献中仅能零星找到其部分性质，或采用未遵循原始统一偏斜正态（SUN）分布参数化的形式，目前尚缺乏系统性研究。本文给出了多元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、潜维度变化、多元偏度和峰度的Mardia测度以及不可识别性问题。这些结果采用的参数化形式可将原始SUN分布作为子模型包含在内，从而便于SUT分布在实际应用中的使用。文中还提供了若干基于SUT分布的模型作为示例。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
