Confidence Intervals for Parameter Variance of Zero-Inflated Two-Parameter Rayleigh Distribution

This study develops confidence and credible intervals for the variance of the zero-inflated two-parameter Rayleigh distribution, a flexible model for non-negative data with excess zeros. Seven approaches are proposed: Bayesian Markov chain Monte Carlo (MCMC), Bayesian highest posterior density (HPD), the standard confidence interval, the approximation normal, the percentile bootstrap, the bootstrap method with standard error, and the generalized confidence interval (GCI). Their performance is assessed through Monte Carlo simulation using coverage probability (CP) and expected length (EL). The results show that the Bayesian HPD interval performs best overall, attaining coverage close to the nominal level while yielding shorter intervals than the alternatives, especially for small samples. The methods are illustrated with road traffic fatality data from Chiang Mai Province, Thailand, recorded in March 2024. These findings support the practical usefulness of the HPD approach for variance interval estimation in zero-inflated continuous models.