On a Corrective Decile-based Confidence Interval Estimator of Mean for Normal and Skewed Distributions

This study addresses an issue with the decile t-confidence interval (dt-CI), which fails to achieve the desired coverage probabilities for large samples or skewed distributions (Mokhtar, Yusof & Sapiri, 2024). The article proposes a new corrective decile t-confidence interval (cdt-CI) that resolves these issues by modifying the decile standard deviation. Simulations using normal, chi-squared, log-normal, and gamma distributions show that the cdt-CI outperforms existing methods, particularly for skewed data, in terms of coverage probability and robustness. The real-life data sets analyzed in this study also support the conclusions of the simulation study.