Interval Estimation for the Difference and Ratio of Variances Under the Zero-Inflated Two-Parameter Rayleigh Distribution

The zero-inflated two-parameter Rayleigh (ZITR) distribution provides a flexible framework for modeling data with excess zeros and positive observations following a two-parameter Rayleigh distribution. It is particularly suitable for right-skewed data and has applications in areas such as road traffic mortality and survival analysis. This study develops and compares several methods for constructing confidence intervals for the difference and ratio of variances from two independent ZITR populations. The considered methods include Bayesian approaches based on Markov Chain Monte Carlo (MCMC) and highest posterior density (HPD) intervals, as well as the generalized confidence interval (GCI), method of variance estimates recovery (MOVER), approximate normal (AN), percentile bootstrap (PB), and bootstrap with standard error (BS). The performance of these methods is evaluated via Monte Carlo simulations under various parameter settings and sample sizes, using coverage probability and expected interval length as performance criteria. The results indicate that the Bayesian HPD method generally performs well across a wide range of scenarios. A real-data application using road traffic mortality data from January 2025 in Chanthaburi and Narathiwat provinces is also presented, demonstrating the practical usefulness of the proposed approaches for comparing the variance structure between the two regions.