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The likely determines the unlikely

Author

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  • Yan, Xiaoyong
  • Minnhagen, Petter
  • Jensen, Henrik Jeldtoft

Abstract

We point out that the functional form describing the frequency of sizes of events in complex systems (e.g. earthquakes, forest fires, bursts of neuronal activity) can be obtained from maximal likelihood inference, which, remarkably, only involve a few available observed measures such as number of events, total event size and extremes. Most importantly, the method is able to predict with high accuracy the frequency of the rare extreme events. To be able to predict the few, often big impact events, from the frequent small events is of course of great general importance. For a data set of wind speed we are able to predict the frequency of gales with good precision. We analyse several examples ranging from the shortest length of a recruit to the number of Chinese characters which occur only once in a text.

Suggested Citation

  • Yan, Xiaoyong & Minnhagen, Petter & Jensen, Henrik Jeldtoft, 2016. "The likely determines the unlikely," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 112-119.
    • Handle: RePEc:eee:phsmap:v:456:y:2016:i:c:p:112-119
    DOI: 10.1016/j.physa.2016.03.027
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    References listed on IDEAS

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    1. Yan, Xiaoyong & Minnhagen, Petter, 2016. "Randomness versus specifics for word-frequency distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 828-837.
    2. Xiaoyong Yan & Petter Minnhagen, 2015. "Maximum Entropy, Word-Frequency, Chinese Characters, and Multiple Meanings," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-19, May.
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    Cited by:

    1. Yan, Xiaoyong & Minnhagen, Petter, 2018. "The dependence of frequency distributions on multiple meanings of words, codes and signs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 554-564.
    2. Yan, Xiaoyong & Yang, Seong-Gyu & Kim, Beom Jun & Minnhagen, Petter, 2018. "Benford’s law and first letter of words," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 305-315.

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    1. Yan, Xiaoyong & Minnhagen, Petter, 2018. "The dependence of frequency distributions on multiple meanings of words, codes and signs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 554-564.
    2. Yan, Xiaoyong & Yang, Seong-Gyu & Kim, Beom Jun & Minnhagen, Petter, 2018. "Benford’s law and first letter of words," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 305-315.
    3. Yan, Xiaoyong & Minnhagen, Petter, 2016. "Randomness versus specifics for word-frequency distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 828-837.

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