Simultaneous Confidence Intervals for Pairwise Differences of Means in Zero-Inflated Rayleigh Distributions with an Application to Road Accident Fatalities Data

This paper develops simultaneous confidence intervals (SCIs) for pairwise differences of means with zero-inflated Rayleigh (ZIR) distributions, a flexible framework for modeling positively skewed data with excess zeros. Closed-form expressions for the ZIR mean are derived, and several competing interval estimation procedures are investigated, including generalized confidence interval (GCI), parametric bootstrap (PB), method of variance estimates recovery (MOVER), delta-method normal approximation, and highest posterior density (HPD) intervals. The finite-sample performance of the proposed SCIs is examined via extensive Monte Carlo simulations, focusing on empirical coverage probabilities (CPs) and average interval lengths (ALs) over a broad range of parameter configurations and zero-inflation levels. A real data application to road accident fatality counts demonstrates the practical utility of the proposed methodology. The results show that the HPD method consistently achieves the most favorable balance between coverage accuracy and interval efficiency. Overall, this study advances reliable simultaneous inference for zero-inflated models commonly encountered in environmental, biomedical, and reliability studies.