Confidence Intervals for the Coefficient of Variation in Delta Inverse Gaussian Distributions

Abstract

The inverse Gaussian distribution is characterized by its asymmetry and right-skewed shape, indicating a longer tail on the right side. This distribution represents extreme values in one direction, such as waiting times, stochastic processes, and accident counts. Moreover, depending on if the accident counts data can occur or not and may have zero value, the Delta Inverse Gaussian (Delta-IG) distribution is more suitable. The confidence interval (CI) for the coefficient of variation (CV) of the Delta-IG distribution in accident counts is essential for risk assessment, resource allocation, and the creation of transportation safety policies. Our objective is to establish CIs of CV for the Delta-IG population using various methods. We considered seven CI construction methods, namely Generalized Confidence Interval (GCI), Adjusted Generalized Confidence Interval (AGCI), Parametric Bootstrap Percentile Confidence Interval (PBPCI), Fiducial Confidence Interval (FCI), Fiducial Highest Posterior Density Confidence Interval (F-HPDCI), Bayesian Credible Interval (BCI), and Bayesian Highest Posterior Density Credible Interval (B-HPDCI). We utilized Monte Carlo simulations to assess the proposed CI technique for average widths (AWs) and coverage probability (CP). Our findings revealed that F-HPDCI and AGCI exhibited the most effective coverage probability and average widths. We applied these methods to generate CIs of CV for accident counts in India.

Keywords

• bootstrap
• generalized confidence interval
• Bayesian credible interval
• fiducial confidence interval
• the highest posterior density interval