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Pure and Applied Geophysics

, Volume 173, Issue 2, pp 709–713 | Cite as

Reply to: “Comment on Pisarenko et al., ‘Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory’” by Mathias Raschke in Pure Appl Geophys (2015)

  • V. F. Pisarenko
  • A. Sornette
  • D. Sornette
  • M. V. Rodkin
Article
  • 101 Downloads
  1. 1.

    Raschke writes (Conclusions, line 4–10):

    In summary, I advise against using the procedures as applied by Pisarenko et al. GPD and GEVD work well only for the extremes of TED or GTED when the block size is very large and/or the threshold is very close to the upper bound magnitude. The crucial point of earthquake magnitudes is the poor convergence of their upper tail to the GPD.

     

As a matter of fact, we did not recommend in our paper to apply our procedures to the TED (truncated exponential distribution) model, which is advocated by Raschke. We applied our method to the Harvard catalog 1977–2006 and to the Fennoscandia catalog 1900–2005, and obtained a quite satisfactory result, in our view. Below, we are providing detailed arguments that support this statement.

We use the same notations as in (R aschke 2016). The data are the same as in (P isarenko et al. 2014): the lower threshold m min = 6.8; sample size (number of main shocks exceeding m min) n = 261. We have fitted the GPD...

Keywords

Earthquake Magnitude Earthquake Catalog Generalize Pareto Distribution Bootstrap Estimate Seismic Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. B. Efron (1973), Bootstrap methods: Another look at the Jack-knife, Ann. Statist., vol. 8, #1, 1–26.Google Scholar
  2. P. Embrechts, C. Kluppelberg, T. Mikosch (1997) Modelling Extremal Events, Springer, Berlin, 1997.Google Scholar
  3. V.F. Pisarenko, M.V. Rodkin (2010) Heavy-Tailed Distributions in Disaster Analysis, Springer, Heidelberg.Google Scholar
  4. V.F. Pisarenko, M.V. Rodkin (2014) Statistical Analysis of Natural Disasters and Related Losses, Springer, Heidelberg.Google Scholar
  5. Pisarenko V. F., Sornette A., Sornette D., and M. V. Rodkin (2014), Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory, Pure Appl. Geophys. 171, 1599–1624.Google Scholar
  6. Raschke, M. (2016) Comment on Pisarenko et al., “Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory”, Pure Appl. Geophys.Google Scholar

Copyright information

© Springer International Publishing 2015

Authors and Affiliations

  • V. F. Pisarenko
    • 1
  • A. Sornette
    • 2
  • D. Sornette
    • 3
    • 4
  • M. V. Rodkin
    • 1
    • 5
  1. 1.Institute of Earthquake Prediction Theory and Mathematical GeophysicsRussian Academy of SciencesMoscowRussia
  2. 2.ETH ZurichSwiss Seismological ServiceZurichSwitzerland
  3. 3.ETH ZurichD-MTECZurichSwitzerland
  4. 4.University of CaliforniaLos AngelesUSA
  5. 5.Institute of Marine Geology and Geophysics, Far East BranchRussian Academy of SciencesYuzhno-SakhalinskRussia

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