A new robust class of multivariate skew distributions is introduced. Practical aspects such as parameter estimation method of the proposed class are discussed, we show that the proposed class can be fitted under a reasonable time frame. Our study shows that the class of distributions is capable to model multivariate skewness structure and does not suffer from the curse of dimensionality as heavily as other distributions of similar complexity do, such as the class of canonical skew distributions. We also derive a nested form of the proposed class which appears to be the most flexible class of multivariate skew distributions in literature that has a closed-form density function. Numerical examples on two data sets, i) a data set containing daily river flow data recorded in the UK; and ii) a data set containing biomedical variables of athletes collected by the Australian Institute of Sports, are demonstrated. These examples further support the practicality of the proposed class on moderate dimensional data sets.

引入了一类新的稳健的多元偏斜分布。讨论了所提出类的参数估计方法等实际方面，我们表明所提出的类可以在合理的时间范围内拟合。我们的研究表明，该分布类别能够​​对多元偏度结构进行建模，并且不会像其他具有类似复杂性的分布（例如典型偏斜分布类别）那样严重地受到维数灾难的影响。我们还导出了所提出类的嵌套形式，它似乎是文献中最灵活的多元偏斜分布类，它具有封闭形式的密度函数。两个数据集的数值示例，i) 一个包含英国记录的每日河流流量数据的数据集；ii) 展示了包含澳大利亚体育研究所收集的运动员生物医学变量的数据集。这些示例进一步支持了建议的类在中等维度数据集上的实用性。