Abstract
In the past and nowadays, hydrology is one of the most natural fields of application for the theory of extremes. This work presents an application of univariate extreme value theory to the study of precipitation in Madeira Island. The method for testing extreme value conditions investigated by Dietrich et al. (Extremes 5:71–85, 2002) was applied to the monthly 1-day maxima precipitation data for the rainy season from seven pluviometric stations maintained by the Portuguese Meteorological Institute. The statistical procedures for the problem of statistical choice of extreme domains of attraction analysed by Neves and Fraga Alves (TEST 16:297–313, 2007) were also applied to each station data set. The results of this analysis indicate the possible k upper extremes to be used for each local sample and the sign of each extreme value index γ.
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Acknowledgements
To the Portuguese Foundation for Science and Technology (FCT), for the financial support through the PhD grant SFRH/BD/39226/2007, financed by national funds of MCTES. To the Center of Statistics and Applications of the University of Lisbon (CEAUL) for the bibliographical support. To the Portuguese Meteorological Institute (IM), namely to Dr. Victor Prior, for providing the precipitation data, and to the University of Madeira for the logistic support. The authors would also like to thank Prof. Dinis Pestana and the anonymous reviewers for their valuable comments and suggestions to improve this paper.
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Gouveia, D., Lopes, L.G., Mendonça, S. (2014). Application of the Theory of Extremes to the Study of Precipitation in Madeira Island: Statistical Choice of Extreme Domains of Attraction. In: Pacheco, A., Santos, R., Oliveira, M., Paulino, C. (eds) New Advances in Statistical Modeling and Applications. Studies in Theoretical and Applied Statistics(). Springer, Cham. https://doi.org/10.1007/978-3-319-05323-3_18
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