Abstract
The work presents statistical methods for estimating the distribution parameters of rare, strong earthquakes. Using the two main theorems of extreme value theory (EVT), the distribution of T-maximum (the maximum magnitude over the time period T). Two methods for estimating the parameters of this distribution are proposed using the Generalized Pareto Distribution (GPD) and the General Extreme Value Distribution (GEV). In addition, the that allow the determination of the distribution of the T-maximum for an arbitrary value of T are proposed. The approach being used clarifies the nature of the instability of the widely accepted M max parameter. In the work, instead of unstable values of the M max parameter, the robust parameter Q T (q), the q level quantile for the distribution of the T-maximum, is proposed to be used. The described method has been applied to the Harvard Catalogue of Seismic Moments of 1977–2006 and to the Magnitude Catalogue for Fennoscandia in 1900–2005. Moreover, the estimates of parameters of the corresponding GPD and GEV distributions, in particular, the most interesting shape parameter and the values of the M max and Q T (q) parameters are given.
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Original Russian Text © V.F. Pisarenko, M.V. Rodkin, 2009, published in Fizika Zemli, 2009, No. 12, pp. 48–59.
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Pisarenko, V.F., Rodkin, M.V. The instability of the M max parameter and an alternative to its using. Izv., Phys. Solid Earth 45, 1081–1092 (2009). https://doi.org/10.1134/S1069351309120052
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DOI: https://doi.org/10.1134/S1069351309120052