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.

Graphic abstract

中文翻译：

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关于q-帕雷托分布：地震的一些性质和应用

摘要

基于超统计形式主义，我们提出了一种新的概率分布。通过转换q指数，我们通过贝克形式主义构造q-帕累托分布。研究了该分布的一些性质，这些性质表明q -Pareto是Pareto分布的适当推广。通过将这种新的q分布应用于较大的地震，我们展示了其在模拟全球地震目录中记录的大地震中的拟合优度。注意，与力矩大小相关的熵\（q_w \）索引的小变化意味着相应\（q_0 \）的指数变化与地震矩相关的指数。我们的结果表明，在对极值建模时，q-帕累托分布比帕累托分布更好。

图形摘要