Modeling both skewness and heavy-tailedness in multivariate data sets is a challenging problem. The main goal of this paper is to introduce a multivariate skew Laplace normal (MSLN) distribution to deal with the issue by providing a flexible model for modeling skewness and heavy-tailedness simultaneously. This distribution will be an alternative to some multivariate skew distributions including the multivariate skew-t-normal (MSTN) distribution introduced by [28]. This is due to the fact that the MSLN distribution has fewer parameters than most of these distributions, which causes computationally advantageous for the MSLN distribution over these distributions. The definition, some distributional properties of this distribution are studied. The maximum likelihood (ML) estimators for the parameters of the MSLN distribution are obtained via the expectation-maximization (EM) algorithm. A simulation study and a real data example are also provided to illustrate the capability of the MSLN distribution for modeling data sets in multivariate settings.

中文翻译：

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多元偏斜拉普拉斯正态分布，用于建模多元数据集中的偏斜和重尾

在多元数据集中对偏度和重尾进行建模是一个具有挑战性的问题。本文的主要目标是引入一个多元偏斜拉普拉斯正态 (MSLN) 分布，通过提供一个灵活的模型来同时建模偏度和重尾性，从而解决该问题。这种分布将替代一些多元偏态分布，包括由 [ 28 ] 引入的多元偏态正态 (MSTN) 分布]。这是因为 MSLN 分布的参数比这些分布中的大多数分布少，这导致 MSLN 分布在计算上优于这些分布。研究了该分布的定义、一些分布性质。MSLN 分布参数的最大似然 (ML) 估计量是通过期望最大化 (EM) 算法获得的。还提供了模拟研究和真实数据示例，以说明 MSLN 分布在多变量设置中对数据集进行建模的能力。