Confidence Intervals for the Mean of Birnbaum-Saunders Distribution with Application to Wind Speed Data

Thailand is dealing with air pollution, particularly from small particulate matter (PM), significantly impacting public health. Wind speed is pivotal in the dispersion of these particles. Due to its unpredictability, we are interested in estimating the confidence interval (CI) for mean wind speed data using a Birnbaum-Saunders (BS) distribution. We have constructed various intervals, Bootstrap confidence interval (BCI), Percentile bootstrap confidence interval (PBCI), Generalized confidence interval (GCI), Bayesian credible interval (BayCI), and The highest posterior density (HPD). Using the R statistical software, a simulation study evaluated their coverage probabilities (CP) and average lengths (AL). GCI emerged as the most effective method overall. With increased sample size and shape parameters, these intervals displayed reduced average lengths. Applying these intervals to wind speed datasets in Nong Prue subdistrict, Chonburi province, Thailand, demonstrated their effectiveness.