Bayesian Estimation for the Single Coefficient of Variation of Zero-Inflated Two-Parameter Rayleigh Distribution

Real data such as road traffic mortality rates and lifetime observations are often zero-inflated and right-skewed. The zero-inflated two-parameter Rayleigh (ZITR) distribution is employed to model such data in this study. The coefficient of variation (CV) is a statistical measure that is used to quantify the relative dispersion of a population, by comparing the standard deviation with the mean. It is widely used to evaluate variability and facilitate comparisons among datasets with different scales or measurement units. This study develops and evaluates seven methods for constructing confidence intervals for the single CV of the ZITR distribution. Three proposed approaches, including Bayesian Markov chain Monte Carlo (MCMC), Bayesian highest posterior density (HPD), and approximate normal (AN) methods, are compared with three existing approaches: generalized confidence interval (GCI), percentile bootstrap (PB), and bootstrap with standard error (BS). Monte Carlo simulations are employed to assess the efficacy of these methods in terms of expected length (EL) and coverage probability (CP). The simulation results show that the HPD method gives acceptable CP with shorter interval lengths than other methods. Moreover, the proposed methods are illustrated with road traffic mortality rates per 100,000 population collected in January 2026 from the Phichit, Suphan Buri, and Prachuap Khiri Khan provinces in Thailand. The results indicate the applicability of the proposed methods for analyzing zero-inflated and right-skewed data in this real-data example.