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Power Law and Entropy Analysis of Catastrophic Phenomena

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  • J. A. Tenreiro Machado
  • Carla M. A. Pinto
  • A. Mendes Lopes

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.

Suggested Citation

  • J. A. Tenreiro Machado & Carla M. A. Pinto & A. Mendes Lopes, 2013. "Power Law and Entropy Analysis of Catastrophic Phenomena," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-10, February.
    • Handle: RePEc:hin:jnlmpe:562320
    DOI: 10.1155/2013/562320
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