Abstract
This chapter is devoted to the study of earthquake size distributions in the uppermost range of extremely rare events. We suggest a new method for statistical estimation of the tail distribution. The method is based on the two main theorems in the theory of extreme values and on the derived duality between the Generalized Pareto Distribution (GPD) and the Generalized Extreme Value distribution (GEV). Particular attention is paid to the adequacy of the widely used parameter M max . This parameter, as will be demonstrated, is very unstable, in particular, in highly seismic regions. Instead of this unstable parameter we suggest a more stable and robust characteristic: the quantile of confidence level q of the random maximum magnitude in a future time interval T, which we shall call the T-maximum. We shall set down methods for practical estimation of such quantiles. Also, some related problems of seismic risk assessment are discussed.
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