Directional multivariate extremes in environmental phenomena Articles uri icon

publication date

  • January 2017

start page

  • 1

end page

  • 15

issue

  • 2

volume

  • 28

international standard serial number (ISSN)

  • 1180-4009

electronic international standard serial number (EISSN)

  • 1099-095X

abstract

  • Several environmental phenomena can be described by different correlated variables that must be considered jointly in order to be more representative of the nature of these phenomena. For such events, identification of extremes is inappropriate if it is based on marginal analysis. Extremes have usually been linked to the notion of quantile, which is an important tool to analyze risk in the univariate setting. We propose to identify multivariate extremes and analyze environmental phenomena in terms of the directional multivariate quantile, which allows us to analyze the data considering all the variables implied in the phenomena, as well as look at the data in interesting directions that can better describe an environmental catastrophe. Because there are many references in the literature that propose extremes detection based on copula models, we also generalize the copula method by introducing the directional approach. Advantages and disadvantages of the nonparametric proposal that we introduce and the copula methods are provided in the paper. We show with simulated and real data sets how by considering the first principal component direction we can improve the visualization of extremes. Finally, two cases of study are analyzed: a synthetic case of flood risk at a dam (a three-variable case) and a real case study of sea storms (a five-variable case).

keywords

  • copulas; flood risk; multivariate directional quantiles; multivariate extremes; principal component analysis; sea storms; flood frequency-analysis; return period; depth functions; copula; distributions; framework; droughts; regions; risks