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.

翻译：我们提出了一种均值泛函，该泛函对任意概率分布均存在，并在左端点有限的分布集合中刻画了帕累托分布的特征。这与均值超额图形成鲜明对比：后者对于均值不存在的分布无意义，且当均值有限而二阶矩不存在时其行为亦非标准。该图的构建基于所谓的"单次巨跳原理"，该原理区分了中等重尾与超重尾分布。我们提出了基于U统计量的尾部函数估计量，并研究了其大样本性质。通过多个损失数据集展示了新图的应用效果。