Article

On the Frequency of Severe Terrorist Events

Journal of Conflict Resolution (Impact Factor: 2.24). 07/2006; 51(1). DOI: 10.1177/0022002706296157
Source: arXiv

ABSTRACT In the spirit of Richardson's original (1948) study of the statistics of deadly conflicts, we study the frequency and severity of terrorist attacks worldwide since 1968. We show that these events are uniformly characterized by the phenomenon of scale invariance, i.e., the frequency scales as an inverse power of the severity, P(x) ~ x^-alpha. We find that this property is a robust feature of terrorism, persisting when we control for economic development of the target country, the type of weapon used, and even for short time-scales. Further, we show that the center of the distribution oscillates slightly with a period of roughly tau ~ 13 years, that there exist significant temporal correlations in the frequency of severe events, and that current models of event incidence cannot account for these variations or the scale invariance property of global terrorism. Finally, we describe a simple toy model for the generation of these statistics, and briefly discuss its implications.

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    • "Power law probability distributions have the relatively simple form of p(x) ∝ x −α (1) where α > 1 and x > 0. The parameter α, is often referred to as the exponent or scaling parameter. Although straightforward, these distributions have gathered scientific interest from many areas, including terrorism, astrophysics, neuroscience, biology, database curation and criminology[7] [13] [1] [21] [2] [9]. "
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    ABSTRACT: Over the last few decades power law distributions have been suggested as forming generative mechanisms in a variety of disparate fields, such as, astrophysics, criminology and database curation. However, fitting these heavy tailed distributions requires care, especially since the power law behaviour may only be present in the distributional tail. Current state of the art methods for fitting these models rely on estimating the cut-off parameter $x_{\min}$. This results in the majority of collected data being discarded. This paper provides an alternative, principled approached for fitting heavy tailed distributions. By directly modelling the deviation from the power law distribution, we can fit and compare a variety of competing models in a single unified framework.
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    • "As a consequence of these findings, researchers claimed that insurgent wars were qualitatively distinct from traditional wars. A coefficient value of ~ a ¼ 2:5 was in concordance with the coefficient value of ~ a ¼ 2:48 AE 0:07 obtained by Clauset et al. [38] on global terrorism. "
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    ABSTRACT: Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.
    Applied Mathematical Modelling 08/2014; 38(15-16). DOI:10.1016/j.apm.2014.01.012 · 2.25 Impact Factor
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    • "Authors applied a PL distribution to Iraq and Colombia wars, with parameter value close to ̃ í µí»¼ = 2.5. A coefficient value of ̃ í µí»¼ = 2.5 was in concordance with the coefficient value of ̃ í µí»¼ = 2.48 ± 0.07 obtained by Clauset et al. [34] on global terrorism. A PL fit to Spanish and American Civil wars revealed a PL parameter value smaller (around ̃ í µí»¼ = 1.7). "
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    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.
    Mathematical Problems in Engineering 01/2013; DOI:10.1155$/$2013$/$562320 · 1.08 Impact Factor
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