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In this short note, I comment on the research of Pisarenko et al. (2014)regarding the extreme value theory and statistics in case of earthquakemagnitudes. The link between the generalized extreme value distribution (GEVD)as an asymptotic model for the block maxima of a random variable and thegeneralized Pareto distribution (GPD) as a model for the peak over thresholds(POT) of the same random variable is presented more clearly. Pisarenko et al.(2014) have inappropriately neglected that the approximations by GEVD and GPDwork only asymptotically in most cases. This applies particularly for thetruncated exponential distribution (TED), being a popular distribution modelfor earthquake magnitudes. I explain why the classical models and methods ofthe extreme value theory and statistics do not work well for truncatedexponential distributions. As a consequence, the classical methods should beused for the estimation of the upper bound magnitude and correspondingparameters. Furthermore, different issues of statistical inference of Pisarenkoet al. (2014) are commented on and alternatives are proposed. Arguments arepresented why GPD and GEVD would work for different types of stochasticearthquake processes in time, and not only for the homogeneous (stationery)Poisson process as assumed by Pisarenko et al. (2014). The crucial point ofearthquake magnitudes is the poor convergence of their tail distribution to theGPD, and not the earthquake process in time.

pure and applied geophysics

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"