Statistical Estimation of Common Percentile in Birnbaum–Saunders Distributions: Insights from PM2.5 Data in Thailand

This study develops approaches for estimating the common percentile of Birnbaum–Saunders (BS) distributions and applies them to daily PM2.5 concentration data from six monitoring stations in Chiang Mai Province, Thailand. Percentiles provide a robust representation of typical pollutant exposure, being less sensitive to outliers and suitable for skewed environmental data. Estimating the same percentile across multiple monitoring sites offers a standardized metric for regional air quality assessment, enabling meaningful comparisons and informing evidence-based environmental policy. Four statistical approaches—Generalized Confidence Interval (GCI), bootstrap, Bayesian, and Highest Posterior Density (HPD)—were employed to construct confidence intervals (CIs) for the common percentile. Simulation studies evaluated the methods in terms of average length (AL) and coverage probability (CP), showing that the GCI approach offers the best balance between precision and reliability. Application to real PM2.5 data confirmed that the BS distribution appropriately models pollutant concentrations and that the common percentile provides a meaningful measure for environmental assessment. These findings highlight the GCI method as a robust tool for constructing CIs in environmental data analysis.