Improving the performance of bootstrap Edgeworth-based confidence interval for the mean of positively skewed distributions

The mean can be an important metric, even when the data distribution is asymmetric. Current confidence intervals for the population mean do not attain the nominal confidence level for small to medium samples drawn from skewed distributions, except for the recently introduced bootstrap Edgeworth-based confidence interval. The limitation of the new method is its potential to produce long intervals for small samples. In this study, we explored various variants of this confidence interval that utilize different estimators of skewness and excess kurtosis. We assessed their performance by analyzing the coverage probability, mean interval length and the coefficient of variation of the length, using small to medium random samples drawn from a range of positively skewed distributions. The performance of four best-performing variants was compared to the bootstrap t, percentile, BC, and BCa confidence intervals. The improved bootstrap Edgeworth-based confidence interval demonstrated superior performance compared to other bootstrap confidence intervals regarding coverage probability, making it a strong recommendation for practical application.