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.
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References
C.W. Anderson, J. Royal Stat. Soc. Ser. B 52, 425 (1990)
C.E. Antoniak, Ann. Stat. 2, 1152 (1974)
J. Beirlant, Y. Goegebeur, J. Segers, J. Teugels, Statistics of Extremes (John Wiley, 2004)
S.G. Coles, An Introduction to Statistical Modeling of Extreme Values (London: Springer-Verlag, 2001)
S.G. Coles, L. Pericchi, Appl. Stat. 52, 405 (2003)
S.R. Dalal, Sankhyā 40, 185 (1978)
S.R. Dalal, G.J. Hall, Ann. Stat. 8, 664 (1980)
A.C. Davison, D.V. Hinkley, Bootstrap Methods and Their Application (Cambridge University Press, 1997)
A.C. Davison, R.L. Smith, J. Royal Stat. Soc. Ser. B 52, 393 (1990)
A.P. Dempster, N.M. Laird, D.B. Rubin, J. Royal Stat. Soc. Ser. B 39, 1 (1977)
L. Fawcett, D. Walshaw, Environmetrics 18, 173 (2007)
T.S. Ferguson, Ann. Stat. 1, 209 (1973)
C.A.T. Ferro, J. Segers, J. Royal Stat. Soc. Ser. B 65, 545 (2003)
L. de Haan, A. Ferreira, Extreme Value Theory: An Introduction (Springer-Verlag, Berlin, 2006)
T.J. Hastie, R.J. Tibshirani, J.H. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction (New York: Springer-Verlag, 2001)
J.E. Heffernan, J.A. Tawn, Z. Zhang, Extremes 10, 57 (2007)
N.L. Hjort, C.C. Holmes, P. Müller, S.G. Walker (eds.), Bayesian Nonparametrics (Cambridge: Cambridge University Press, 2010)
T. Hsing, Stoch. Proc. and their Applications 26, 297 (1987)
M.C. Larsen, G.F. Wieczorek, L.S. Eaton, B.A. Morgan, H. Torres-Sierra, Eos, Trans. Amer. Geophys. Union 47, 572 (2001)
J. Pickands, Ann. Stat. 3, 119 (1975)
G. Schwarz, Ann. Stat. 6, 461 (1978)
R.L. Smith, I. Weissman, Characterization and estimation of the multivariate extremal index (1996) (unpublished)
M. Süveges, Extremes 10, 41 (2007)
M. Süveges, Statistical analysis of clusters of extreme events, Ph.D. thesis, École Polytechnique Fédérale de Lausanne (2009)
M. Süveges, A.C. Davison, Ann. Appl. Stat. 4, 203 (2010)
Z. Zhang, Ann. Inst. Stat. Math. 60, 121 (2008)
Z. Zhang, Stat. Infer. Stoch. Proc. 12, 89 (2009)
Z. Zhang, R.L. Smith, J. Appl. Prob. 41, 1113 (2004)
Z. Zhang, R.L. Smith, J. Stat. Plann. Infer. 140, 1135 (2010)
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Süveges, M., Davison, A.C. A case study of a “Dragon-King”: The 1999 Venezuelan catastrophe. Eur. Phys. J. Spec. Top. 205, 131–146 (2012). https://doi.org/10.1140/epjst/e2012-01566-6
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DOI: https://doi.org/10.1140/epjst/e2012-01566-6