Comparing Confidence Intervals for the Mean of Symmetric and Skewed Distributions

In context-aware decision analysis, mean can be an important measure, even when the distribution is skewed. Previous comparative studies showed that it is a real challenge to construct a confidence interval that performs well for highly skewed data. In this study, we propose new confidence intervals for the population mean based on Edgeworth expansion that include both skewness and kurtosis corrections. We compared existing and newly proposed confidence intervals for a range of samples from symmetric and skewed distributions of varying levels of kurtosis. Using Monte Carlo simulations, we evaluated the performance of these intervals based on the coverage probability, mean length, and standard deviation of the length. The proposed bootstrap Edgeworth-based confidence interval outperformed other confidence intervals in terms of coverage probability for both symmetric and skewed distributions and can be recommended for general use in practice.