Distributions conditioned on extrapolated events via copula and extreme value theory

In an interaction between road users, the proximity and speed are two interdependent dimensions which can be captured by a type of multivariate distribution called Copula. Copula requires all marginal distribution functions to be known. However, finding the marginal distribution of the proximity dimension is challenging, as its histogram usually contains several peaks. We partition the outcome space in a way that extreme value theory can be used as a tool to approximate the target marginal distribution in the tail region. In traffic safety research, such approach has the following advantages:•The approach can approximate the distribution in the region in which the density is monotone.•Via copula and extreme value theory, it is possible to find the conditional distribution while the conditions are not present in the data set.