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A pentatonic classification of extreme events

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  • Eliazar, Iddo
  • Cohen, Morrel H.

Abstract

In this paper we present a classification of the extreme events – very small and very large outcomes – of positive-valued random variables. The classification distinguishes five different categories of randomness, ranging from the very ‘mild’ to the very ‘wild’. In analogy with the common five-tone musical scale we term the classification ‘pentatonic’. The classification is based on the analysis of the inherent Gibbsian ‘forces’ and ‘temperatures’ existing on the logarithmic scale of the random variables under consideration, and provides a statistical-physics insight regarding the nature of these random variables. The practical application of the pentatonic classification is remarkably straightforward, it can be performed by non-experts, and it is demonstrated via an array of examples.

Suggested Citation

  • Eliazar, Iddo & Cohen, Morrel H., 2015. "A pentatonic classification of extreme events," Chaos, Solitons & Fractals, Elsevier, vol. 74(C), pages 3-14.
    • Handle: RePEc:eee:chsofr:v:74:y:2015:i:c:p:3-14
    DOI: 10.1016/j.chaos.2014.07.010
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    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401, December.
    2. Alfarano, Simone & Milakovic, Mishael, 2008. "Does classical competition explain the statistical features of firm growth?," Economics Letters, Elsevier, vol. 101(3), pages 272-274, December.
    3. repec:cup:cbooks:9781107013445 is not listed on IDEAS
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