Confidence Intervals for the Ratio between Two Means of Birnbaum-Saunders Distributions

Abstract

In this study, we introduced several methods to estimate confidence intervals for the ratio between means of Birnbaum-Saunders (BirSau) distributions. These methods encompassed the generalized confidence interval (GCI), bootstrap confidence interval (BCI), percentile bootstrap confidence interval (PBCI), Bayesian credible interval (BayCrI), and the highest posterior density (HPD). We conducted a Monte Carlo simulation to assess their performance, focusing on coverage probabilities and average widths. The simulation results revealed that the HPD method consistently delivered strong results for small and medium sample sizes across various scenarios. However, in the case of larger samples, the BCI method emerged as the most effective option. It was observed that as the sample size increased, the average widths of the proposed confidence intervals tended to decrease. Furthermore, we applied these methods to establish confidence intervals for the ratio between the means of wind speed datasets originating from two separate industrial regions in Thailand: Samut Prakan and Rayong province. The results obtained from this real-data application closely aligned with the findings derived from our simulation results.