Confidence Intervals for Ratio of Percentiles of Birnbaum-Saunders Distributions and Its Application to PM2.5 in Northern Thailand

Abstract

In the statistical literature, the Birnbaum-Saunders distribution has garnered considerable attention as an important fatigue life distribution for engineers. This distribution finds applications in medicine, engineering, and science. A percentile denotes a threshold below which a designated percentage of scores or data points are situated. In particular cases, percentiles are the preferred choice over mean and variance, especially when dealing with skewed data. This paper investigates confidence intervals for the ratio of percentiles of Birnbaum-Saunders distributions. It discusses the generalized fiducial confidence interval, Bayesian credible interval, and the highest posterior density intervals using a prior distribution with partial information and a proper prior with known hyperparameters. To compare the performance of these confidence intervals, the study employs coverage probability and average length measurements. Monte Carlo simulation via the R package is used to calculate the coverage probability and average length. The results indicate that the highest posterior density interval using a prior distribution with partial information outperforms the other confidence intervals. Finally, the paper presents the results of the simulation study and applies them in the field of environmental sciences.