Two Parameters Generalized Skew Normal Distribution

Behrouz Fathi-Vajargah, Setareh Payk


In practice, using skew normal distribution (SN) seems better than exact/usual normal distribution since in nature, we cannot find the exact normal distribution. Here, we first study and review single variable skew normal distribution using one parameter then we extend this distribution using two parameters  to have a better control on behavior of the fact normal distribution. We show that this generalization of the SN distribution by , then we present some useful properties of this distribution and also prove some important theorems for introducing the generalized skew normal distribution, and describe an algorithm for generating it. Finally, we show some properties of GSN distribution based on conditional and marginal distribution mixed by independent random variables and parameters . Some important results are follow: if  be independent standard normal random variables and . Then  Also, we show that if then  The introduced algorithm can be implemented to generate GSN distribution.


parameters generalized skew normal distributions- Moment generating function

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