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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 562320, 10 pages
http://dx.doi.org/10.1155/2013/562320
Review Article

Power Law and Entropy Analysis of Catastrophic Phenomena

1Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto (ISEP), Rua Dr. António Bernardino de Almeida, 431, 4200-072 Porto, Portugal
2Institute of Engineering, Polytechnic of Porto (ISEP) and Center of Mathematics of the University of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072 Porto, Portugal
3UISPA, IDMEC-Polo FEUP, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal

Received 17 September 2012; Accepted 13 December 2012

Academic Editor: József Kázmér Tar

Copyright © 2013 J. A. Tenreiro Machado et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Catastrophic events, such as wars and terrorist attacks, tornadoes and hurricanes, earthquakes, tsunamis, floods and landslides, are always accompanied by a large number of casualties. The size distribution of these casualties has separately been shown to follow approximate power law (PL) distributions. In this paper, we analyze the statistical distributions of the number of victims of catastrophic phenomena, in particular, terrorism, and find double PL behavior. This means that the data sets are better approximated by two PLs instead of a single one. We plot the PL parameters, corresponding to several events, and observe an interesting pattern in the charts, where the lines that connect each pair of points defining the double PLs are almost parallel to each other. A complementary data analysis is performed by means of the computation of the entropy. The results reveal relationships hidden in the data that may trigger a future comprehensive explanation of this type of phenomena.