1887

Abstract

Summary

The theory of extreme values is a correct way for study of probability of occurrence of rare largest events. We use the Generalized Pareto Distribution (GPD) and the General Extreme Value Distribution (GEV). The unknown parameters of these distributions can be determined from the empirical data using the maximal likelihood approach. However, this method is optimal only for the case of fairly large (N>200–300) samples. We used numerical modeling and revealed that for the case of a small samples, the method of quantile is preferable in using the GPD approach, and the statistical moments method is preferable when using the GEV approach. Three data sets characterizing the distribution of earthquakes in subduction zones, regions of intracontinental seismicity, and in the mid-oceanic ridge zones were compiled and the parameters of the corresponding GPD and GEV distributions were determined. To obtain the similar results in the scale of the general seismic zoning problem we suggest to use the local characteristics of intensity of earthquake flow and the b-value and to characterize the tail behavior from data for the much wider areas. The preliminary results are discussed.

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/content/papers/10.3997/2214-4609.201801799
2018-05-14
2020-11-28
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References

  1. EmbrechtsP., Kluppelberg, C., & Mikosch, T.
    [1997]. Modelling extremal events (p. 645). Berlin: Springer.
  2. Hosking, J. R., Wallis, J. R., & Wood, E. F.
    [1985]. Estimation of the generalized extreme-value distribution by the method of probability-weighted moments. Technometrics, 27, 251–261.
    [Google Scholar]
  3. Kagan, Y. Y.
    [1999]. Universality of the seismic moment-frequency relation. Pure Applied Geophysics, 155, 537–573.
    [Google Scholar]
  4. Kagan, Y.Y.
    [2002]. Seismic moment distribution revisited: I. Statistical results. Geophys Journal Int148:520–541
    [Google Scholar]
  5. Pisarenko, V., & Rodkin, M.
    [2010]. Heavy-tailed distributions in disaster analysis. Advances in natural and technological hazards research, Volume 30. Dordrecht: Springer.
    [Google Scholar]
  6. Pisarenko, V.F., Rodkin, M.V.
    [2017]. The Estimation of Probability of Extreme Events for Small Samles. Pure Appl. Geophys., 174, 4, 1547–1560, DOI 10.1007/s00024‑017‑1495‑0.
    https://doi.org/10.1007/s00024-017-1495-0 [Google Scholar]
  7. Pisarenko, V.F., Rodkin, M. V., Rukavishnikova, T. A.
    [2017]. Probability Estimation of Rare Extreme Events in the Case of Small Samples: Technique and Examples of Analysis of Earthquake Catalogs. Izvestiya, Physics of the Solid Earth. Vol. 53, No. 6, pp. 805–818.
    [Google Scholar]
  8. Smith, R.
    [1990]. Extreme value theory. In W.Ledermann (Ed.), Handbook of Applicable Mathematics, Supplement (pp.437–472). Chichester: Wiley.
    [Google Scholar]
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