Metastatistics of Extreme Values and its Application in Hydrology

TL;DR

This paper introduces the metastatistics of extreme events, a new statistical framework for accurately estimating the frequency of extreme events in inhomogeneous data, demonstrated through hydrological rainfall data.

Contribution

The paper proposes a novel metastatistics approach that improves predictions of extreme event frequencies over traditional methods like GEV, especially in inhomogeneous datasets.

Findings

Metastatistics accurately predicts extreme event frequencies.

Traditional GEV approach fails with inhomogeneous data.

Application to rainfall data demonstrates practical utility.

Abstract

We present a novel statistical treatment, the "metastatistics of extreme events", for calculating the frequency of extreme events. This approach, which is of general validity, is the proper statistical framework to address the problem of data with statistical inhomogeneities. By use of artificial sequences, we show that the metastatistics produce the correct predictions while the traditional approach based on the generalized extreme value distribution does not. An application of the metastatistics methodology to the case of extreme event to rainfall daily precipitation is also presented.