In this paper, the shape mixtures of the skew Laplace normal (SMSLN) distribution is introduced as a flexible extension of the skew Laplace normal distribution which is also a heavy-tailed distribution. The SMSLN distribution includes an extra shape parameter, which controls skewness and kurtosis. Some distributional properties of this distribution are derived. Besides, we propose finite mixtures of SMSLN distributions to model both skewness and heavy-tailedness in heterogeneous data sets. The maximum likelihood estimators for parameters of interests are obtained via the expectation–maximization algorithm. We also give a simulation study and examine a real data example for the numerical illustration of proposed estimators.

在本文中，引入了偏斜拉普拉斯正态分布（SMSLN）的形状混合体，作为偏斜拉普拉斯正态分布的柔性扩展，它也是一个重尾分布。SMSLN分布包括一个额外的形状参数，该参数控制偏斜度和峰度。得出该分布的一些分布特性。此外，我们提出了SMSLN分布的有限混合，以对异构数据集中的偏度和重尾度进行建模。兴趣参数的最大似然估计是通过期望最大化算法获得的。我们还进行了仿真研究，并研究了一个真实的数据示例，用于对估计量的数值说明。