How to estimate the probability of rare long-distance trips

The vehicle distances travelled by individual users can very strongly between different days. This is particularly problematic for electric vehicles since trips larger than the electric range clearly reduce the vehicle's utility. Here we estimate the number of days with driving distance larger than a given threshold for individual users based on their observed driving behaviour. The general formalism is developed and estimates for the main observable and standard errors are derived based on the assumption of individual log-normal distributed daily vehicle kilometres travelled. Numerical simulations of driving profiles demonstrate the validity and accuracy of the analytical results.