Generalized Confidence Interval for Percentile of Delta Birnbaum–Saunders Distribution

Delta Birnbaum–Saunders distribution has both zero and positive values, with positive values following a Birnbaum–Saunders distribution and zero observations following a binomial distribution. This study constructs a confidence interval for the percentile of the Delta Birnbaum–Saunders distribution using the generalized confidence interval approach and compares it with the bootstrap approach, the highest posterior density approach based on the bootstrap method, the Bayesian approach, and the highest posterior density approach based on the Bayesian method. Monte Carlo simulations are used to evaluate the performance of these confidence intervals. The results show that the generalized confidence interval approach is effective for constructing CIs for the percentiles of the Delta Birnbaum–Saunders distribution. Additionally, when the sample size is large, both the Bayesian approach and the highest posterior density approach based on the Bayesian method are viable alternatives. These approaches are demonstrated using daily wind speed data in Prachin Buri province, Thailand.