New Approach to Estimation of Probability of Rare Extreme Events for the Case of Small Samples: Application to Seismic Zoning Problem
V.F. Pisarenko and M.V. Rodkin
Event name: 17th International Conference on Geoinformatics - Theoretical and Applied Aspects
Session: Mathematical Methods and Computer Technologies in Geophysics and Geology
Publication date: 14 May 2018
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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.