On testing the skew normal distribution by using Shapiro-Wilk test

The skew normal (SN) family of distributions includes the normal distribution as a particular case as well as a wide variety of skew densities. Because of its tractability and flexibility for modeling both symmetric and skew data sets, the SN distribution has plenty of applications in finance, diverse engineering fields and medicine, among others. In this paper, a data transformation to approximately normal variables is used for testing the null hypothesis that a random sample follows a SN distribution with unknown parameters. Formulae obtained by interpolation methods are provided for approximating the critical values of the proposed procedure for a range of sample sizes, avoiding the use of tables and/or resampling methods. The test preserves the nominal test size and turns out to be competitive in terms of power against existing tests for the same problem. Several data sets are considered in order to illustrate the plausibility of the SN distribution for modeling the probability behavior of real data.