Abstract
Natural hazards, such as big earthquakes, affect the lives of thousands of people at all levels. Extreme-value analysis is an area of statistical analysis particularly concerned with the systematic study of extremes, providing an useful insight to fields where extreme values are probable to occur. The characterization of the extreme seismic activity is a fundamental basis for risk investigation and safety evaluation. Here we study large earthquakes in the scope of the Extreme Value Theory. We focus on the tails of the seismic moment distributions and we propose to estimate relevant parameters, like the tail index and high order quantiles using the geometric-type estimators. In this work we combine two approaches, namely an exploratory oriented analysis and an inferential study. The validity of the assumptions required are verified, and both geometric-type and Hill estimators are applied for the tail index and quantile estimation. A comparison between the estimators is performed, and their application to the considered problem is illustrated and discussed in the corresponding context.
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Acknowledgements
ACMF is partially supported by FCT grant SFRH/BPD/66174/2009 and LC is supported by FCT grant SFRH/BD/60642/2009. All three authors are supported by FCT project PTDC/MAT/120346/2010. Research funded by the European Regional Development Fund through the programme COMPETE and by the Portuguese Government through the FCT—Fundação para a Ciência e a Tecnologia under the project PEst—C/MAT/UI0144/2013. The authors also thank the referees for their comments.
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Brito, M., Cavalcante, L., Freitas, A.C.M. (2015). Modeling of Extremal Earthquakes. In: Bourguignon, JP., Jeltsch, R., Pinto, A., Viana, M. (eds) Mathematics of Energy and Climate Change. CIM Series in Mathematical Sciences, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-319-16121-1_3
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DOI: https://doi.org/10.1007/978-3-319-16121-1_3
Publisher Name: Springer, Cham
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