Multiple comparisons of the dispersion of PM2.5 in several locations utilizing simultaneous confidence intervals for all pairwise differences between the coefficients of variation of inverse Gaussian distributions

Abstract

The presence of PM2.5 (particulate matter 2.5) poses a significant threat to human health. Urban activities are where PM2.5 is predominantly produced, and the built environment may have an impact on how it forms and spreads. To analyze PM2.5 data, one can use the coefficient of variation of inverse Gaussian distribution. This study aims to generate simultaneous confidence intervals using the generalized confidence interval, the adjusted generalized confidence interval, the fiducial confidence interval, and the highest posterior density confidence interval methods for all pairs between the coefficients of variation of inverse Gaussian distributions. By using a simulation of Monte Carlo, the effectiveness of the simultaneous confidence interval approaches was evaluated with a focus on two crucial metrics: coverage probabilities and average lengths. The findings demonstrated that the coverage probability conditions were satisfied by the confidence interval obtained by the adjusted generalized confidence interval and the highest posterior density confidence interval methods. The effectiveness of the suggested strategies was shown using PM2.5 data from five Bangkok, Thailand areas.