An Extension of the Epsilon-Skew-Normal Distribution

This article is related with the probabilistic and statistical properties of an parametric extension of the so-called epsilon-skew-normal (ESN) distribution introduced by Mudholkar and Hutson (2000 Mudholkar , G. S. , Hutson , A. D. ( 2000 ). The epsilon-skew-normal distribution for analyzing near-normal data . J. Statist. Plann. Infer. 83 : 291 – 309 .Crossref], Web of Science ®] , Google Scholar]), which considers an additional shape parameter in order to increase the flexibility of the ESN distribution. Also, this article concerns likelihood inference about the parameters of the new class. In particular, the information matrix of the maximum likelihood estimators is obtained, showing that it is non singular in the special normal case. Finally, the statistical methods are illustrated with two examples based on real datasets.