Estimation of the Common Mean of Zero-Inflated Inverse Gaussian Distributions: Application to Road Accident Fatalities in Thailand

This study addresses the estimation of the common mean for the zero-inflated inverse Gaussian (ZIIG) distributions, a problem not previously explored. The performance of four interval estimation approaches was evaluated: the generalized confidence interval (GCI), parametric bootstrap, Bayesian, and highest posterior density (HPD). Simulation studies under varying sample sizes, zero-inflation probabilities, mean values, and shape parameters revealed notable differences in coverage probability (CP) and average length (AL). For small samples, the GCI and parametric bootstrap approaches often under-covered, particularly in highly skewed or heavily zero-inflated cases. In contrast, Bayesian and HPD intervals generally maintained coverage closer to the nominal 0.95 level, albeit with longer intervals. As sample size increased, all methods approached nominal coverage and produced shorter intervals, improving precision. Overall, the Bayesian and HPD approaches demonstrated strong robustness across conditions, with HPD intervals frequently achieving accurate coverage with shorter lengths. Finally, the proposed approaches were applied to real-world data on road accident fatalities in Thailand.