Abstract
Based on the superstatistical formalism, we propose a new probability distribution. By means of a transformation of the q-exponential, we construct the q-Pareto distribution by Beck formalism. Some properties of this distribution are studied which show that the q-Pareto is a proper generalization of the Pareto distribution. By applying this new q-distribution to larger earthquakes, we show its goodness-of-fit to model great earthquakes recorded in global earthquake catalogs. It is noted that a small change in the entropic $$q_w$$ index associated with the moment magnitude implies an exponential change in the corresponding $$q_0$$ index associated with the seismic moments. Our results suggest that q-Pareto distribution is a better candidate than Pareto distribution when modeling extreme values.
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