Confidence Intervals for the Variance and Standard Deviation of Delta-Inverse Gaussian Distributions with Application to Traffic Mortality Count

Abstract

The inverse Gaussian (IG) distribution exhibits asymmetry and right skewness. This distribution presents values uniformly, encompassing wait length, stochastic processes, and rates of accident occurrences. The delta-inverse Gaussian (delta-IG) distribution is suitable for modeling traffic accident data as a mortality count, especially in cases when accidents may not occur. The confidence interval (CI) for the variance and standard deviation of the delta-IG distribution for the accident count is crucial for evaluating risk, allocating resources, and formulating enhancement protocols for transportation safety. We aim to construct confidence intervals for variance and standard deviation in the delta-IG population using several approaches: Adjusted GCI (AGCI), Parametric Bootstrap Percentile CI (PBPCI), fiducial CI (FCI), and Bayesian credible interval (BCI). The AGCI, PBPCI, and FCI will be utilized with estimation methods for proportions which are VST, Wilson’s score, and Hannig approaches. Monte Carlo simulations were evaluated, and the suggested confidence interval approach was employed for the average width (AW) and coverage probability (CP). The findings demonstrated that the AGCI based on the VST method employed successful approaches, as seen in their CP and AW. We employed these approaches to produce CIs for the variance and S.D. of the mortality count in Bangkok.