Estimating the Confidence Interval for the Common Coefficient of Variation for Multiple Inverse Gaussian Distributions

The inverse Gaussian distribution is a two-parameter continuous probability distribution with positive support, which is used to account for the asymmetry of the positively skewed data that are often seen when modeling environmental phenomena, such as PM2.5 levels. The coefficient of variation is often used to assess variability within datasets, and the common coefficient of variation of several independent samples can be used to draw inferences between them. Herein, we provide estimation methods for the confidence interval for the common coefficient of variation of multiple inverse Gaussian distributions by using the generalized confidence interval (GCI), the fiducial confidence interval (FCI), the adjusted method of variance estimates recovery (MOVER), and the Bayesian credible interval (BCI) and highest posterior density (HPD) methods using the Jeffreys prior rule. The estimation methods were evaluated based on their coverage probabilities and average lengths, using a Monte Carlo simulation study. The findings indicate the superiority of the GCI over the other methods for nearly all of the scenarios considered. This was confirmed for a real-world scenario involving PM2.5 data from three provinces in northeastern Thailand that followed inverse Gaussian distributions.