A novel hypothesis testing method of skew-normal distribution based on the fourth-order moment property

A novel method for testing skew-normal distribution is proposed, and this method is called the fourth-order moment test (FOMT). It is a statistic constructed based on the fourth-order moment of the standard skew-normal distribution. We compared FOMT with the Kolmogorov-Smirnov test (KS test), the Anderson-Darling test (AD test), AS test, and W test, both of which generate random numbers of skew-normal distribution by stochastic representing and compares the probability of the Type I error for tests. The true distributions of different alternative hypotheses are simulated by Monte Carlo (MC), and the power functions of the tests are calculated. Monte Carlo simulations show that FOMT has a significant advantage in power function. A real data application is analyzed by the proposed methodology.