Modified Maximum Likelihood Estimations of the Epsilon-Skew-Normal Family

In this work, maximum likelihood (ML) estimations of the epsilon-skew-normal (ESN) family are obtained using an EM-algorithm to modify the ordinary estimation already used and solve some of its problems within issues. This family can be used for analyzing the asymmetric and near-normal data, so the skewness parameter epsilon is the most important parameter among others. We have shown that the method has better performance compared to the method in G.S. Mudholkar, A.D. Hutson, J. Statist. Plann. Infer. 83 (2000), 291–309, especially in the strong skewness and small samples. Performances of the proposed ML estimates are shown via a simulation study and some real datasets under some statistical criteria as a way to illustrate the idea.