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

Abstract

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.

Keywords:

• Anderson-Darling test
• Fourth-order moment test
• Kolmogorov-Smirnov test
• Power function
• Skew-normal distribution

Acknowledgment

The authors thank the Editor and two referees for their valuable comments that have greatly improved the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China (12261051).