  We propose a mean functional which exists for any probability distributions,
and which characterizes the Pareto distribution within the set of distributions
with finite left endpoint. This is in sharp contrast to the mean excess plot
which is not meaningful for distributions without existing mean, and which has
a nonstandard behaviour if the mean is finite, but the second moment does not
exist. The construction of the plot is based on the so called principle of a
single huge jump, which differentiates between distributions with moderately
heavy and super heavy tails. We present an estimator of the tail function based
on $U$-statistics and study its large sample properties. The use of the new
plot is illustrated by several loss datasets.
