The full-tails gamma distribution applied to model extreme values

TL;DR

This paper introduces a gamma distribution extension to better model extreme values, addressing anomalies in Pareto-based models and demonstrating its application in climate and operational risk data analysis.

Contribution

It proposes a novel full-tails gamma distribution that explains deviations from Pareto law in extreme value modeling.

Findings

The extended gamma model captures anomalies in Pareto distributions.

Application to climate data shows improved modeling of tropical cyclone occurrences.

Operational risk analysis benefits from the new distribution in aggregate loss modeling.

Abstract

In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory. The results are useful to certain phenomena that are fitted by the Pareto distribution but, at the same time, they present a deviation from this law for very large values. Two examples of data analysis with the new model are provided. The first one is on the influence of climate variability on the occurrence of tropical cyclones. The second one on the analysis of aggregate loss distributions associated to operational risk management.