Evaluation of Robust Confidence Interval for the Standard Deviation under Non-Normality

Accepted April 2026

Abstract

This paper evaluates the performance of Abu-Shawiesh et al. (2011)’s robust confidence interval for the population standard deviation which was designed to achieve a coverage probability close to a nominal of 100(1−α)%, particularly for skewed distributions. A simulation study was conducted to evaluate the performance of this method, and a discrepancy was discovered between the simulation results and those reported by the original authors. Specifically, for skewed distributions, the procedure exhibited very poor coverage-approaching zero in some cases. Motivated by this finding, this paper introduces a modified version of the robust method that provides coverage probabilities much closer to the nominal level of 100(1 − α)%. The modification builds upon the approach of Abu-Shawiesh et al. (2011) but incorporates an adjustment to account for skewness. Results from Monte Carlo simulations using both normal and non-normal distributions indicate that the modified method produces confidence intervals with substantially improved coverage probabilities compared to the original procedure, particularly under skewed distributions.