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
Received:
12
September
2020
Accepted:
18
December
2020
Published online:
22
January
2021
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.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2021