An Extension of the Epsilon-Skew-Normal Distribution

Abstract

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), 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.

Keywords:

• Asymmetry
• Bimodality
• Kurtosis
• Maximum likelihood estimation
• Non singular information matrix

Mathematics Subject Classification:

• Primary 60E05
• Secondary 62E10

Acknowledgments

The authors thank one anonymous referee for constructive comments. The first author was partially supported by Grant FONDECYT 1085241; the second by Grant DIUDA-221151; and the third by Grant FONDECYT 1060727.