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In this article, we propose the joint location, scale and skewness models of the skew Laplace normal (SLN) distribution as an alternative model for the joint modelling location, scale and skewness models of the skew-t-normal distribution when the data set contains both asymmetric and heavy-tailed observations. We obtain the maximum likelihood estimators for the parameters of the joint location, scale and skewness models of the SLN distribution using the expectation–maximization algorithm. The performance of the proposed model is demonstrated by a simulation study and a real data example.

Joint Modelling of the Location, Scale and Skewness Parameters of the Skew Laplace Normal Distribution