Simultaneous Confidence Intervals for All Pairwise Differences between the Means of Multiple Zero-Inflated Birnbaum–Saunders Distributions

Wind energy offers a naturally occurring, unlimited resource that preserves the environment. Using wind speed as a renewable energy source generates electricity and helps reduce environmental impacts. Achieving maximum efficiency in electricity production requires a consistent wind speed. However, since wind speed varies naturally, it is unpredictable. Wind speed can have positive values but can be zero on days without wind. Therefore, using the zero-inflated Birnbaum–Saunders (ZI-BirSau) distribution to estimate wind speed can provide valuable insights. This study proposes methods for estimating simultaneous confidence intervals (SCIs) for all pairwise differences between the means of multiple ZI-BirSau distributions. The study employs the generalized confidence interval (GCI), bootstrap confidence interval (BCI), and the method of variance estimate recovery (MOVER) approaches. Specifically, we apply the GCI and BCI approaches, incorporating the estimation of zero proportions using the variance stabilized transformation (VST) and Wilson approaches. The study uses a Monte Carlo simulation to compare their performance in terms of coverage probabilities (CPs) and average widths (AWs). The simulation results show that the GCI based on the VST approach performs better than other approaches, except for large sample sizes, where the BCI based on the VST approach proves more effective. The proposed approaches tested wind speed data from the Ko Sichang weather station in Chonburi, Thailand, yielding results consistent with the simulation study. This result confirms that the proposed approaches effectively estimate SCIs for all pairwise differences between the means of multiple ZI-BirSau distributions.