When does the mean excess plot look linear?

TL;DR

The paper investigates when the mean excess plot appears linear, concluding that only the generalized Pareto family of distributions exhibits this property under certain conditions, aiding risk analysis.

Contribution

It proves that the linearity of the mean excess plot uniquely characterizes the generalized Pareto family under specific assumptions.

Findings

Only the generalized Pareto family has a linear mean excess plot under certain conditions.

The linearity property can be used to identify generalized Pareto distributions in risk analysis.

Provides theoretical justification for using mean excess plots in distribution fitting.

Abstract

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.