Abstract: The zero-inflated Rayleigh distribution combines zero values and a standard Rayleigh distribution that represents positive values. Percentiles are widely used tools for measuring data, particularly in skewed continuous datasets. This study aims to construct confidence intervals (CIs) for the percentile of the zero-inflated Rayleigh distribution. The proposed approaches include the generalized confidence interval (GCI), normal approximation (NA), and the percentile bootstrap confidence interval (PBCI). The zero-inflation probability is estimated using the variance-stabilizing transformation (VST), Wilson's Score, and Hannig’s methods. Their performances were evaluated using Monte Carlo simulations in R programming, comparing coverage probabilities (CPs) and average lengths (ALs). The results indicate that the GCI based on the VST outperformed the other methods. Additionally, the proposed CIs were applied to car accident mortality data in central Thailand to evaluate their practical efficacy.

Keywords: Rayleigh distribution, zero inflation, percentile, generalized confidence interval, normal approximation, percentile bootstrap confidence interval

Pages: 102-115