The Beyondpareto Command for Optimal Extreme-Value Index Estimation

Abstract

In this article, we introduce the command beyondpareto, which estimates the extreme-value index for distributions that are Pareto-like, that is, whose upper tails are regularly varying and eventually become Pareto. The estimation is based on rank-size regressions, and the threshold value for the upper-order statistics included in the final regression is determined optimally by minimizing the asymptotic mean squared error. An essential diagnostic tool for evaluating the fit of the estimated extreme-value index is the Pareto quantile–quantile plot, provided in the accompanying command pqqplot. The usefulness of our estimation approach is illustrated in several real-world examples focusing on the upper tail of German wealth and city-size distributions.