Modeling the Traffic Accident Data Using a Convenient Lognormal Diffusion Process

Abstract

Aims: Theories of diffusion process play an important role in safety traffic applications. The purpose of this paper is to introduce a methodology capable for fitting the yearly traffic accidents in Kuwait. More specifically, a lognormal diffusion model is specified to be capable to fit and explicitly addressing the variations in the yearly traffic accidents in Kuwait during the period 2002-2013. Estimation results using the maximum likelihood estimation and the goodness of fit using the sample autocorrelation function clearly demonstrated the appropriateness of the estimated lognormal diffusion model. Study Design: A rigorous and mathematically sound model is specified to study the yearly total number of traffic accidents in Kuwait. Place and Duration of Study: Department of Quantitative Methods and Information Systems, College of Business Administration, Kuwait University, Kuwait, during the year 2016. Methodology: A lognormal diffusion process is considered and estimation is done using the MLE method and goodness of fit using sample ACF and partial ACF are also used to prove the capability and the appropriateness of the suggested lognormal diffusion model to fit the yearly traffic accidents data in Kuwait during the period 2002-2013.              Results: To estimate the previously specified lognormal diffusion model, we use the yearly observations of the total number of accident data in Kuwait from 2002 to 2013 were obtained from the Kuwait Traffic Police Department. The maximum likelihood estimates of model parameters are given by  = 0.0342,  = 0.00125, =  0.00125 and  = 0.03482. Using the fitted model, we predict the yearly number of accidents for the period from 2014 to 2020. The capability of the model is supported by the residual analysis through the autocorrelation and the normal probability plots. Conclusion: This study provided a methodology capable and convenient to fit the traffic accident data and departs from the traditional before-and-after regression techniques and the time series analysis and developed a diffusion model that explicitly accounts for the variations in the total number of accidents.