  In order to assess future damage caused by natural disasters, it is desirable
to estimate the damage caused by single events. So called damage functions
provide -- for a natural disaster of certain magnitude -- a specific damage
value. However, in general, the functional form of such damage functions is
unknown. We study the distributions of recorded flood damages on extended
scales and deduce which damage functions lead to such distributions when the
floods obey Generalized Extreme Value statistics and follow Generalized Pareto
distributions. Based on the finding of broad damage distributions we
investigate two possible functional forms to characterize the data. In the case
of Gumbel distributed extreme events, (i) a power-law distribution density with
an exponent close to 2 (Zipf's law) implies an exponential damage function;
(ii) stretched exponential distribution densities imply power-law damage
functions. In the case of Weibull (Frechet) distributed extreme events we find
correspondingly steeper (less steep) damage functions.
