Estimating the expected number of crashes with traffic conflicts and the Lomax Distribution - A theoretical and numerical exploration.

This paper justifies the Lomax distribution for counterfactual modeling of the probability of crash given a traffic conflict. The pre-crash process leading to a conflict or a crash as the result of a failure is discussed as this conceptualization is the basis for proposing a simple model of the probability of a crash at the moment when a conflict is still progressing. Then, a model applicable to heterogeneous conditions is derived; and the model's relevance, useful properties, and limitations are discussed. The published concepts and study results that support the derived model are provided in the paper. The existing Maximum Likelihood Estimate (MLE) method and the Probability-Weighted Moments (PWM) method of estimating the probability of crash and the expected number of crashes based on the proposed theory are presented. Then, a new Single Parameter Estimation (SPE) method is proposed and evaluated with extensive Monte Carlo experiments. The performance of the MLE, PWM, and SPE methods are compared. The SPE method is found more accurate and efficient than the other two methods. Unlike the benchmark methods, the proposed method produces real estimates in each case. The most important outcome of the presented study is confirmation that traffic conflicts claimed based on sufficiently small threshold separation (such as Time to Collision) allow unbiased estimation of the expected number of crashes during the conflicts observation period. A practical procedure of estimating safety is proposed that identifies the longest suitable threshold separation for each case based on the trends in the estimation results.