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

  • Regular Article - Statistical and Nonlinear Physics
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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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Data Availability Statement

This manuscript has no associated data or the data will not be deposited [Authors’ comment: We have used two database: USGS Science Data (https://earthquake.usgs.gov/earthquakes/search/) and ISC, International Seismological Center (ISC) (http://www.isc.ac.uk/iscgem/request_catalogue.php).]

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Acknowledgements

Thanks to the Direction of Research of Development of the University of La Serena (DIDULS), and the Post-graduate program of the Department of Physics and Astronomy of the University of La Serena.

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Authors and Affiliations

  1. Departamento de Física y Astronomía, Facultad de Ciencias, Universidad de La Serena, La Serena, Chile

    Erick de la Barra & Pedro Vega-Jorquera

  2. Departamento de Matemáticas, Facultad de Ciencias, Universidad de La Serena, La Serena, Chile

    Erick de la Barra

  3. Instituto de Investigación Multidisciplinaria en Ciencia y Tecnología, Universidad de La Serena, La Serena, Chile

    Pedro Vega-Jorquera

Authors
  1. Erick de la Barra
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  2. Pedro Vega-Jorquera
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Both authors have contributed equally to the research work as well as both have approved the final manuscript.

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Correspondence to Pedro Vega-Jorquera.

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de la Barra, E., Vega-Jorquera, P. On q-pareto distribution: some properties and application to earthquakes. Eur. Phys. J. B 94, 32 (2021). https://doi.org/10.1140/epjb/s10051-021-00045-7

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