A note on rescalings of the skew-normal distribution

In this article, we show that certain skew-normal parametric statistical models are a result of rescalings of the skew normal model studied by Azzalini (1985). Using this procedure we define a class of skew-normal distributions and we study its moment, skewness and kurtosis coefficients. At the end of this article we will use this class of distribution to make some extensions of the skew-normal model.