Estimates of extremes in the best of all possible worlds

In applied hydrology the question of the probability of exceeding a certain value occurs regularly. Often it is in a context where extrapolation from a relatively short time series is needed. It is well known that in its simplest form extreme value theory applies to independent identically distributed random variables. It is also well known that more advanced theory allows for some degrees of correlation and that techniques for coping with trends are available. However, the problem of extrapolation remains. To isolate the effect of extrapolation we generate synthetic time series of length 20, 50 and 100 from known distributions to derive empirical distributions for the 1:100 and 1:1000 exceedance.Water ManagementCivil Engineering and Geoscience