Kesen Wang , Maicon J. Karling , Reinaldo B. Arellano-Valle , Marc G. Genton
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引用次数: 0
Abstract
The unified skew- (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.
统一偏斜正态分布（SUT）是一种灵活的参数多元分布，它考虑了数据的偏斜度和重尾。它的一些性质散见于文献或参数化中，与统一偏态正态分布（SUN）的原始参数化不同，但缺乏系统的研究。本研究提出了多元 SUT 分布的明确性质，如随机表示、矩、SUN 尺度混合表示、线性变换、可加性、边际分布、典型形式、二次形式、条件分布、潜维变化、多元偏度和峰度的 Mardia 度量以及不可识别性问题。这些结果以参数化的形式给出，可以还原为原始 SUN 分布的子模型，从而方便了 SUT 的应用。本文提供了几个基于 SUT 分布的模型以作说明。
期刊介绍：
Founded in 1971, the Journal of Multivariate Analysis (JMVA) is the central venue for the publication of new, relevant methodology and particularly innovative applications pertaining to the analysis and interpretation of multidimensional data.
The journal welcomes contributions to all aspects of multivariate data analysis and modeling, including cluster analysis, discriminant analysis, factor analysis, and multidimensional continuous or discrete distribution theory. Topics of current interest include, but are not limited to, inferential aspects of
Copula modeling
Functional data analysis
Graphical modeling
High-dimensional data analysis
Image analysis
Multivariate extreme-value theory
Sparse modeling
Spatial statistics.
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