Confidence Intervals for Differences between Percentiles of Two Weibull Distributions: An Application to Wind Speed Data

This study aims to analyze, develop, and compare methods for assessing the difference between percentiles of Weibull distributions. Confidence intervals for the difference between percentiles are constructed to evaluate the accuracy and reliability of group comparisons. The statistical methods considered include the Generalized Confidence Interval (GCI), Bootstrap, and Bayesian approaches, which are used to construct and compare confidence intervals for differences between percentiles. The performance of the confidence interval is evaluated based on coverage probability and average interval width to determine the precision and efficiency of each approach. The result indicated that the Bayesian highest posterior density (Baye-HPD) interval outperforms others. Real-world wind speed data, categorized by location, are employed to demonstrate the practical applicability of the proposed methods.