  In risk analysis, the mean excess plot is a commonly used exploratory
plotting technique for confirming iid data is consistent with a generalized
Pareto assumption for the underlying distribution, since in the presence of
such a distribution thresholded data have a mean excess plot that is roughly
linear. Does any other class of distributions share this linearity of the plot?
Under some extra assumptions, we are able to conclude that only the generalized
Pareto family has this property.
