Eur. Phys. J. Special Topics 205, 131-146 (2012)
https://doi.org/10.1140/epjst/e2012-01566-6

Regular Article

A case study of a “Dragon-King”: The 1999 Venezuelan catastrophe

¹ University of Geneva, ISDC Data Centre for Astrophysics, Chemin d’Ecogia 16, 1290 Versoix, Switzerland
² École Polytechnique Fédérale de Lausanne, EPFL-FSB-MATHAA-STAT, Station 8, 1015 Lausanne, Switzerland

^a e-mail: Maria.Suveges@unige.ch
^b e-mail: Anthony.Davison@epfl.ch

Received: 23 November 2011
Revised: 9 March 2012
Published online: 1 May 2012

Abstract

We describe a failure of standard extremal models to account for a catastrophic rainfall event in the coastal regions of Venezuela on 14–16 December 1999, due both to inaccurate tail modelling and to an inadequate treatment of clusters of rare events. We investigate this failure, using a Dirichlet mixture model to approximate a form of moving maximum process that should provide accurate models for wide classes of extremal behaviour. This so-called M3-Dirichlet model may be fitted using an EM algorithm, and provides a reasonable explanation for the properties of the data, in terms of a seasonally-varying mixture of types of extreme rainfall clusters.