On the Fernández–Steel distribution: Inference and application

In this article, we perform statistical inference on a skew model that belongs to a class of distributions proposed by Fernández and Steel (1998). Specifically, we introduce two ways to represent this model by means of which moments and generation of random numbers can be obtained. In addition, we carry out estimation of the model parameters by moment and maximum likelihood methods. Asymptotic inference based on both of these methods is also produced. We analyze the expected Fisher information matrix associated with the model and highlight the fact that this does not have the singularity problem, as occurs with the corresponding information matrix of the skew-normal model introduced by Azzalini (1985). Furthermore, we conduct a simulation study to compare the performance of the moment and maximum likelihood estimators. Finally, an application based on real data is carried out.