This work contributes to study the application of extreme value theory (EVT) in road safety analysis, estimating the risk of being involved in an entering–circulating collision in single-lane roundabouts. Detailed trajectory data of the vehicles were derived from a driving simulator experiment, and the time-to-collision (TTC) was used as a surrogate measure of safety. Three EVT approaches were applied, tested and compared: (1) the Generalized Extreme Value distribution used in the block maxima (BM) approach, (2) the Generalized Pareto Distribution used in the peak-over-threshold approach (POT), with negated-TTC (nTTC), and (3) shifted-reciprocal-TTC (srTTC). Case-study results analysis showed that BM and POT with shifted-reciprocal-TTC confidence intervals included the number of observed crashes, while POT with negated-TTC did not include it. According to these findings, both BM and POT-with-shifted-reciprocal-TTC appear promising and deserve further attention in order to develop effective ready-to-practice crash prediction models, useful in intersection design and operational analysis.

Emerging international transportation system (ITS) and sensing technologies allow collecting of large amounts of high‐quality traffic data in highways, which can be used for road safety analysis. With this kind of data, it is possible to apply extreme value theory (EVT), which is gaining interest in the field of road safety, thanks to its ability to produce quick and reliable safety evaluations. EVT can estimate the probability of extreme events (i.e. road crashes) from relatively short observation periods, using surrogate measures of safety in place of crash data. In this work, EVT is applied for a large‐scale case study in two motorways, located in north‐eastern Italy. Vehicle‐by‐vehicle information was collected using microwave radars in 19 motorways cross‐sections for one year, and time‐to‐collision was calculated for each pair of consecutive vehicles. A six‐year crash database of the toll road was used to validate model results. For each cross‐section, two traditional approaches, block‐maxima and peak‐over‐threshold, were applied to estimate EVT parameters. Both approaches produced reliable predictions of annual rear‐end collisions; in particular, in about 90% of the cross‐sections, the observed number of crashes fell within the 95% confidence interval of the predicted number of crashes.