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Abstract <p>Wind energy offers a naturally occurring, unlimited resource thatpreserves the environment. Using wind speed as a renewable energysource generates electricity and helps reduce environmentalimpacts. Achieving maximum efficiency in electricity productionrequires a consistent wind speed. However, since wind speed variesnaturally, it is unpredictable. Wind speed can have positivevalues but can be zero on days without wind. Therefore, using thezero-inflated Birnbaum–Saunders (ZI-BirSau) distribution toestimate wind speed can provide valuable insights. This studyproposes methods for estimating simultaneous confidence intervals(SCIs) for all pairwise differences between the means of multipleZI-BirSau distributions. The study employs the generalizedconfidence interval (GCI), bootstrap confidence interval (BCI),and the method of variance estimate recovery (MOVER) approaches.Specifically, we apply the GCI and BCI approaches, incorporatingthe estimation of zero proportions using the variance stabilizedtransformation (VST) and Wilson approaches. The study uses a MonteCarlo simulation to compare their performance in terms of coverageprobabilities (CPs) and average widths (AWs). The simulationresults show that the GCI based on the VST approach performsbetter than other approaches, except for large sample sizes, wherethe BCI based on the VST approach proves more effective. Theproposed approaches tested wind speed data from the Ko Sichangweather station in Chonburi, Thailand, yielding results consistentwith the simulation study. This result confirms that the proposedapproaches effectively estimate SCIs for all pairwise differencesbetween the means of multiple ZI-BirSau distributions.</p>

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

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Natchaya Ratasukharom,
  • Sa-Aat Niwitpong,
  • Suparat Niwitpong

摘要

Abstract

Wind energy offers a naturally occurring, unlimited resource thatpreserves the environment. Using wind speed as a renewable energysource generates electricity and helps reduce environmentalimpacts. Achieving maximum efficiency in electricity productionrequires a consistent wind speed. However, since wind speed variesnaturally, it is unpredictable. Wind speed can have positivevalues but can be zero on days without wind. Therefore, using thezero-inflated Birnbaum–Saunders (ZI-BirSau) distribution toestimate wind speed can provide valuable insights. This studyproposes methods for estimating simultaneous confidence intervals(SCIs) for all pairwise differences between the means of multipleZI-BirSau distributions. The study employs the generalizedconfidence interval (GCI), bootstrap confidence interval (BCI),and the method of variance estimate recovery (MOVER) approaches.Specifically, we apply the GCI and BCI approaches, incorporatingthe estimation of zero proportions using the variance stabilizedtransformation (VST) and Wilson approaches. The study uses a MonteCarlo simulation to compare their performance in terms of coverageprobabilities (CPs) and average widths (AWs). The simulationresults show that the GCI based on the VST approach performsbetter than other approaches, except for large sample sizes, wherethe BCI based on the VST approach proves more effective. Theproposed approaches tested wind speed data from the Ko Sichangweather station in Chonburi, Thailand, yielding results consistentwith the simulation study. This result confirms that the proposedapproaches effectively estimate SCIs for all pairwise differencesbetween the means of multiple ZI-BirSau distributions.