This study develops and evaluates simultaneous confidence interval procedures for all pairwise differences of coefficients of variation under delta-inverse Gaussian distributions. The objective is to provide reliable comparative inference for relative variability in zero-inflated and highly skewed data, where standard normal-based methods may be unreliable. Five approaches were studied and compared in terms of coverage probabilities and average widths: generalized confidence interval, adjusted generalized confidence interval, fiducial confidence interval, method of variance estimates recovery, and normal approximation. A Monte Carlo simulation study was conducted under varying shape parameters, zero-inflation probabilities, sample sizes, and numbers of populations (k = 3, 6, and 10). Although most methods produced CPs near the nominal 0.95 level, meaningful differences emerged when both coverage accuracy and interval efficiency were considered. The AGCI method consistently delivered stable coverage across parameter settings and remained robust as dimensionality increased. The MOVER approach achieved competitive coverage while frequently yielding narrower intervals. In contrast, GCI occasionally showed mild undercoverage, and FCI tended to produce overly wide intervals. An empirical application to zero-inflated mortality data supports the simulation findings. Overall, AGCI and MOVER provide reliable and practical tools for simultaneous inference on differences in CVs across delta-IG populations.
Khumpasee et al. (Thu,) studied this question.