Confidence intervals for the difference and ratio of two coefficients of variation of delta-inverse Gaussian distributions

The inverse Gaussian (IG) distribution demonstrates asymmetry and right skewness. This distribution exhibits values uniformly, including waiting duration, stochastic processes, and accident occurrence rates. The delta inverse Gaussian (delta-IG) distribution is suitable for modeling traffic accident data as a count of fatalities, particularly in instances where incidents may not occur. The confidence interval (CI) for the difference and ratio of two coefficients of variation of delta-IG distributions in accident frequencies is essential for assessing risk, distributing resources, and developing improvement strategies for transportation safety. Our objective is to establish confidence intervals for the difference and ratio of the coefficients of variation of two delta-IG populations through various methods: Adjusted GCI (AGCI), Fiducial CI (FCI), Bayesian Credible Interval (BCI), Method of Variance Estimates Recovery (MOVER), and Normal Approximation (NA). Monte Carlo simulations were assessed, and the proposed confidence interval approach was implemented for average width (AW) and coverage probability (CP). The results indicated that the AGCI and MOVER methods employed efficient procedures, as evidenced by their CP and AW. We utilized these approaches to generate confidence intervals for the difference and ratio of two coefficient of variations of delta-IG distributions in the mortality count data from the central region of Thailand.