Confidence Intervals for the Mean and Difference of Means of Birnbaum-Saunders Distributions with Application to Wind Speed Data

Abstract

This paper proposes the confidence intervals for the mean and difference of means of Birnbaum-Saunders (BirSau) distributions based on the Bootstrap confidence interval (BCI), Percentile bootstrap confidence interval (PBCI), Generalized confidence interval (GCI), Bayesian credible interval (BayCrI) and the highest posterior density (HPD). The simulation study used R statistical software to evaluate the coverage probabilities and average lengths. The concerning results of the mean suggest that HPD is the recommended method for constructing confidence intervals in the BirSau distributions, except for small sample sizes where the GCI method proves more efficient. For the difference of means, PBCI emerges as the preferred way to construct confidence intervals, except in some cases where small sample sizes with the HPD method are more efficient. Moreover, the average lengths of these proposed confidence intervals decreased as both sample size and shape parameters increased. To illustrate the effectiveness of the suggested confidence intervals, we applied them to wind speed datasets collected in Ayutthaya and Ratchaburi provinces, Thailand.