B0744
Title: Assessing the skew normality hypothesis using the Shapiro-Wilk test
Authors: Elizabeth Gonzalez-Estrada - Colegio de Postgraduados (Mexico) [presenting]
Aurora Monter-Pozos - Colegio de Postgraduados (Mexico)
Abstract: The skew-normal family of distributions includes the normal distribution as a particular case as well as a variety of skew densities. This class of distributions has plenty of applications in finance, engineering, medicine and genomics, to mention a few disciplines. A procedure for testing the null hypothesis that a random sample follows a skew-normal distribution with unknown parameters is presented. The technique consists of transforming the data to approximately normally distributed observations and then assessing the normality hypothesis using the Shapiro-Wilk test. Since the null distribution of the test statistic does not have a closed form, it is approximated by simulation for different values of the skewness parameter. Intensive simulation studies considering different sample sizes indicate that the quantile function of the test statistic under the null hypothesis behaves like a non-increasing function of the absolute value of the skewness parameter. Based on this finding, the critical region of the test corresponding to a given test size can be identified. Formulae obtained by interpolation methods in terms of normal quantiles are provided for approximating the critical values of the test for a range of sample sizes, avoiding the use of tables. The results of simulation studies under various scenarios indicate that the test preserves the nominal test size, and it is a competitive method in terms of power compared to other methods for the same problem.
