A Flexible Skew-Generalized Normal Distribution

Abstract

Skew-symmetric distributions of various types have been the center of attraction by many researchers in the literature. In this article, we will introduce a uni/bimodal generalization of the Azzalini's skew-normal distribution which is indeed an extension of the skew-generalized normal distribution obtained by Arellano-Valle et al. (2004). Our new distribution contains more parameters and thus it is more flexible in data modeling. Indeed, certain univariate case of the so called flexible skew-symmetric distribution of Ma and Genton (2004) is also a particular case of our proposed model. We will first study some basic distributional properties of the new extension, such as its distribution function, limiting behavior and moments. Then, we will investigate some useful results regarding its relation with other known distributions, such as student's t and skew-Cauchy distributions. In addition, we will present certain methods to generate the new distribution and, finally, we shall apply the model to a real data set to illustrate its behavior comparing to some rival models.

Keywords:

• Fitting
• Flexible skew-normal distribution
• Skew-normal distribution
• Stochastic representation

Mathematics Subject Classification:

• 60E
• 62E

Acknowledgments

The authors sincerely thank two anonymous referees for their valuable comments that led to improvement of this article. The authors are also grateful to the Graduate Office of the University of Isfahan for their support.