Bayesian Estimation of the Difference and Ratio of the Coefficients of Variation Under the Zero-Inflated Two-Parameter Rayleigh Distribution

The coefficient of variation (CV) is a widely used unit-free measure for comparing variability across two or more populations, even when the data are measured on different scales. In this study, we investigate confidence and credible interval estimation for the difference and ratio of CVs from the zero-inflated two-parameter Rayleigh (ZITR) distribution, which accommodates excess zeros and positively skewed observations through a two-component mixture structure. Several interval estimation methods are proposed, including the Bayesian Credible Interval (BCI), Bayesian Highest Posterior Density (HPD), and Approximate Normal (AN) approaches. Their performances are compared with established methods, namely the Generalized Confidence Interval (GCI), Method of Variance Estimates Recovery (MOVER), Percentile Bootstrap (PB), and Bootstrap with Standard Error (BS). A Monte Carlo simulation study is conducted to evaluate the methods in terms of coverage probability (CP), Monte Carlo standard error (MCSE) of the estimated coverage probability, and expected length (EL). The simulation results indicate that the HPD method provides the best overall performance, achieving coverage probabilities close to the nominal level with small MCSE values, indicating stable simulation estimates, while maintaining relatively short interval lengths. The proposed confidence interval methods were further applied to district-level road traffic fatality rates (per 100,000 population) in Uttaradit and Mae Hong Son provinces, Thailand. The road traffic fatality data included fatalities occurring in March 2026. The fatality rates were calculated based on the district-level population size to enable comparisons across districts with different population scales.