The beyondpareto command for optimal extreme value index estimation

Abstract

This paper introduces the command beyondpareto, which estimates the extreme value index for distributions that are Pareto-like, i.e. 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 (AMSE). An essential diagnostic tool for evaluating the fit of the estimated extreme value index is a Pareto quantile-quantile (QQ) 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 the German wealth and city size distribution.

Publication
The Stata Journal, forthcoming

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