On an Extended Version of Skew Generalized Normal Distribution and Some of its Properties

Abstract

Here we consider a new class of asymmetric normal distributions as a generalization of the skew normal distribution of Azzalini (1985) and the skew generalized normal distribution of Arellano-Valle et al. (2004). Several properties of this new class of distributions are derived and there by obtained the corresponding properties of the location scale extended family of the new class of distributions. The estimation of the parameters of the location scale extended class of distributions is also briefly discussed.

Keywords:

• Asymmetric distributions
• Characteristic function
• Plurimodality
• Reliability measures
• Skew normal distributions
• Skew generalized normal distributions

Mathematics Subject Classification:

• 60E05
• 60E10