The purpose of this paper is to propose some test statistics for testing the skewness parameter of a distribution, not limited to a normal distribution. Since a theoretical comparison is not possible, a simulation study has been conducted to compare the performance of the test statistics. We have compared both parametric methods (classical method with normality assumption) and non-parametric methods (bootstrap in Bias Corrected Standard Method, Efron’s Percentile Method, Hall’s Percentile Method and Bias Corrected Percentile Method). Our simulation results indicate that the power of the tests differ significantly across sample sizes, the choice of alternative hypotheses and methods one choose. When the data are generated from a normal distribution, both classical method and Efron’s Percentile Method can attain a nominal size of 0.05, while other bootstrap methods cannot. However, for a skewed distribution, bootstrap methods show higher power with larger sample sizes whereas the classical method only performs well when the sample size is small.
Guo, Yawen and Golam Kibria, B. M.
On Some Statistics for Testing the Skewness in a Population: An Empirical Study,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 12,
2, Article 6.
Available at: https://digitalcommons.pvamu.edu/aam/vol12/iss2/6