Abstract In this paper, we propose a matrix extension of the scale and shape mixtures of multivariate skew normal distributions and present some particular cases of this new class. We also present several formal properties of this class, such as the marginal distributions, the moment generating function, the distribution of linear and quadratic forms, and the selection and stochastic representations. In addition, we introduce the matrix variate tail conditional expectation measure and derive this risk measure for the scale and shape mixtures of matrix variate extended skew normal distributions. We present an efficient EM-type algorithm for the computation of maximum likelihood estimates of parameters in some special cases of the proposed class. Finally, we conduct a small simulation study and fit various special cases of the new class to a real dataset.

中文翻译：

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矩阵变量扩展偏斜正态分布的尺度和形状混合

摘要 在本文中，我们提出了多元偏态正态分布的尺度和形状混合的矩阵扩展，并展示了这个新类别的一些特殊情况。我们还介绍了此类的几个形式属性，例如边缘分布、矩生成函数、线性和二次形式的分布以及选择和随机表示。此外，我们引入了矩阵变量尾部条件期望度量，并为矩阵变量扩展偏斜正态分布的尺度和形状混合导出了该风险度量。我们提出了一种有效的 EM 类型算法，用于在所提出的类的某些特殊情况下计算参数的最大似然估计。最后，