Browsing by Author "Felgueiras, Miguel Martins"
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- Explaining the seismic moment of large earthquakes by heavy and extremely heavy tailed modelsPublication . Felgueiras, Miguel MartinsThe search of physical laws that explain the energy released by the great magnitude earthquakes is a relevant question, since as a rule they cause heavy losses. Several statistical distributions have been considered in this process, namely heavy tailed laws, like the Pareto distribution with shape parameter α ≈ 0. 6667. Yet, for the usually considered Californian region (where earthquakes with moment magnitude, MW, greater than 7. 9 were never registered) the Pareto distribution with index near the above mentioned seems to have a "too heavy" tail for explaining the bigger earthquakes seismic moments. Usually an exponential tapper is applied to the distribution right tail (above the so called corner seismic moment), or another distribution is considered to explain these high seismic moment data (like another Pareto with different shape parameter). The situation is different for other regions where seisms of larger magnitudes do occur, leading to data sets for which heavy or even extremely heavy tailed models are appropriated. The purpose of this paper is to reduce the seismic moment, M0, of the very large earthquakes to particular heavy and extremely heavy tailed distributions. Using world seismic moment information, we apply Pareto, Log-Pareto and extended slash Pareto distributions to the data, truncated for M0 ≥ 1021 Nm and for M0 ≥ 1021. 25 Nm. For these great seisms we conclude that extended slash Pareto is a promising alternative to the more traditional Pareto and Log-Pareto distributions as a candidate to the real model underlying the data.
- Gaussian Scale MixturesPublication . Felgueiras, Miguel Martins; Martins, João Paulo; Santos, Rui Filipe; European Society of Computational Methods in Sciences and Engineering (ESCMSE)In this paper we present a parsimonious approximation of a Gaussian mixture when its components share a common mean value, i.e. a scale mixture. We show that a shifted and scaled Student’s t -distribution can be approximated to this type of mixture, and use the result to develop a hypothesis test for the equality of the components mean value. A simulation study to check the quality of the approximation is also provided, together with an application to logarithmic daily returns.