Eur. Phys. J. B (2021) 94: 32
https://doi.org/10.1140/epjb/s10051-021-00045-7

Regular Article - Statistical and Nonlinear Physics

On q-pareto distribution: some properties and application to earthquakes

¹ Departamento de Física y Astronomía, Facultad de Ciencias, Universidad de La Serena, La Serena, Chile
² Departamento de Matemáticas, Facultad de Ciencias, Universidad de La Serena, La Serena, Chile
³ Instituto de Investigación Multidisciplinaria en Ciencia y Tecnología, Universidad de La Serena, La Serena, Chile

^b pvega@userena.cl

Received: 12 September 2020
Accepted: 18 December 2020
Published online: 22 January 2021

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 index associated with the moment magnitude implies an exponential change in the corresponding index associated with the seismic moments. Our results suggest that q-Pareto distribution is a better candidate than Pareto distribution when modeling extreme values.