Pareto Models for the Energy Released in Earthquakes

In this paper we explore Pareto based distributions to deal with the energy released by the major seisms. This is a relevant problem because great earthquakes can cause heavy losses, both human and material. The standard Pareto distribution, despite being usually well fitted to the data concerning the energy released by seisms, reveals some lack of fit when dealing with the energy released by the great earthquakes. Besides the more traditional Pareto and Log-Pareto, we also consider the Extended Slash Pareto (ESP) and the Location-Scale Pareto Mixture (LSPM) distributions in this work. For the less studied ESP and LSPM distributions, we present the parameters estimators and perform a simulation study in order to evaluate the estimators performance under different scenarios. Thenceforth, the four distributions are applied to two datasets (catalogs) containing information on the seisms magnitude, which has a direct connection to the energy released by the earthquakes (seismic moment). The used catalogs are considered as conveniently accurate and updated, and are being used in recent works. In conclusion, the Pareto distribution still is appropriate to fit this kind of data, but other distributions emerge as better models. The Log-Pareto distributions led to higher fitting p-values than the Pareto distribution, and LSPM also emerges as a strong competitor. LSPM is better fitted to the greatest observations and therefore gives a more accurate prevision for the energy released by the greater earthquakes. Key–Words: Pareto based models, great earthquakes, seismic moment Received: March 3, 2020. Revised: April 15, 2020. Accepted: May 6, 2020. Published: May 18, 2020.