Shifted Gamma-Generalized Pareto Distribution model to map the safety continuum and estimate crashes

Safety continuum plays an important role in the development of traffic conflict techniques. This study proposes a shifted Gamma-Generalized Pareto Distribution (GPD) model to map the whole safety continuum and then estimate crashes. Two important model parameters, the threshold and shifted value, are discussed in detail. The threshold, which is mapped as the boundary to distinguish conflicts and normal events, is estimated simultaneously with other four Gamma-GPD parameters by Bayesian approach. The shifted value, which is introduced by shifted reciprocal mapping and mapped as the boundary to distinguish conflicts and crashes, is determined by a crash-based approach. The proposed model is applied to estimate crashes related to lane change maneuvers on freeways, and the Bayesian approach is also compared with the classical maximum likelihood estimation approach. More accurate and less uncertain estimated crashes are obtained through the Bayesian approach, and this also shows the superiority of shifted reciprocal mapping approach over the linear mapping approaches. Meanwhile, the estimated model parameters show that the boundary to distinguish conflicts and crashes is consistent while the boundaries to distinguish conflicts and normal events might be varied across different segments.