The Applications of Generalized Poisson Distribution in Accident Data Analysis

Abstract

Accident counts at a site are usually assumed to be Poisson distributed. However, past studies have shown that many variations exist in the accident data, which often results in the data to be either overdispersed or underdispersed. Thus, a Generalized Poisson (GP) distribution is introduced as an alternative distribution for accident counts data. The GP distribution can cater the data that are more or less dispersed than required by Poisson distribution. This paper examines the appropriateness of using GP distribution in accident data analysis and Empirical Bayes (EB) safety estimation method. The results show that the GP distribution is a better fitting model than Poisson distribution such that, generally, the goodness-of-fit statistics studied (SSE and χ²) are significantly improved. When the GP distribution is used to modify the EB method, it is able to improve the prediction of safety as compared to the original EB method.