Comparison of Some Confidence Intervals for Estimating the Skewness Parameter of a Distribution

Abstract

Several methods have been proposed to calculate interval estimators for estimating the skewness of a distribution. Since they considered in different times and under different simulation conditions, their performance are not comparable as a whole. In this paper an attempt has been made to review some existing estimators and compare them under the same simulation condition. In particularly, we consider and compare both classical (normality assumed) and non-parametric (bias-corrected standard bootstrap, Efron’s percentile bootstrap, Hall’s percentile bootstrap and bias-corrected percentile bootstrap) interval estimators for estimating the skewness of a distribution. A simulation study has been made to compare the performance of the estimators under normal, right and left skewed distributions. Both average widths and coverage probabilities are considered as a criterion of the good estimators. We have found a significant difference in the performance of classical and bootstrap estimators in all cases. Based on the simulation results we have found that both classical estimators and bootstrap estimators work well in terms of coverage probability when data comes from a normal distribution, although bootstrap methods tend to give smaller intervals in that case. When data comes from skewed distributions, bootstrap methods perform better than classical methods in terms of coverage. Amongst the bootstrap methods, the bias corrected percentile interval had the best coverage consistently for skewed data. One real life data sets are analyzed to illustrate the findings of the paper.