@article{WietzkeMerzGerlitzetal.2020,
  author    = {Wietzke, Luzie M. and Merz, Bruno and Gerlitz, Lars and Kreibich, Heidi and Guse, Bj{\"o}rn and Castellarin, Attilio and Vorogushyn, Sergiy},
  title     = {Comparative analysis of scalar upper tail indicators},
  series = {Hydrological sciences journal = Journal des sciences hydrologiques},
  volume    = {65},
  journal   = {Hydrological sciences journal = Journal des sciences hydrologiques},
  number    = {10},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {0262-6667},
  doi       = {10.1080/02626667.2020.1769104},
  pages     = {1625 -- 1639},
  year      = {2020},
  abstract  = {Different upper tail indicators exist to characterize heavy tail phenomena, but no comparative study has been carried out so far. We evaluate the shape parameter (GEV), obesity index, Gini index and upper tail ratio (UTR) against a novel benchmark of tail heaviness - the surprise factor. Sensitivity analyses to sample size and changes in scale-to-location ratio are carried out in bootstrap experiments. The UTR replicates the surprise factor best but is most uncertain and only comparable between records of similar length. For samples with symmetric Lorenz curves, shape parameter, obesity and Gini indices provide consistent indications. For asymmetric Lorenz curves, however, the first two tend to overestimate, whereas Gini index tends to underestimate tail heaviness. We suggest the use of a combination of shape parameter, obesity and Gini index to characterize tail heaviness. These indicators should be supported with calculation of the Lorenz asymmetry coefficients and interpreted with caution.},
  language  = {en}
}