Anticipating catastrophes through extreme value modelling.

*(English)*Zbl 1111.62366Summary: When catastrophes strike it is easy to be wise after the event. It is also often argued that such catastrophic events are unforeseeable, or at least so implausible as to be negligible for planning purposes. We consider these issues in the context of daily rainfall measurements recorded in Venezuela. Before 1999 simple extreme value techniques were used to assess likely future levels of extreme rainfall, and these gave no particular cause for concern. In December 1999 a daily precipitation event of more than 410 mm, almost three times the magnitude of the previously recorded maximum, caused devastation and an estimated 30000 deaths. We look carefully at the previous history of the process and offer an extreme value analysis of the data - with some methodological novelty - that suggests that the 1999 event was much more plausible than the previous analyses had claimed. Deriving design parameters from the results of such an analysis may have had some mitigating effects on the consequences of the subsequent disaster. The themes of the new analysis are simple: the full exploitation of available data, proper accounting of uncertainty, careful interpretation of asymptotic limit laws and allowance for non-stationarity. The effect on the Venezuelan data analysis is dramatic. The broader implications are equally dramatic; that a naïve use of extreme value techniques is likely to lead to a false sense of security that might have devastating consequences in practice.

##### MSC:

62P12 | Applications of statistics to environmental and related topics |

62G32 | Statistics of extreme values; tail inference |

##### Software:

ismev
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\textit{S. Coles} and \textit{L. Pericchi}, J. R. Stat. Soc., Ser. C, Appl. Stat. 52, No. 4, 405--416 (2003; Zbl 1111.62366)

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