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CI_POWERTAIL: MATLAB function to test for 'dragon kings' vs. 'black swans'


  • Joanna Janczura
  • Rafal Weron


[CI_LO,CI_HI]=CI_POWERTAIL(DATA,ALPHA,TAIL) calculates confidence intervals of significance level ALPHA for a power law fitted to the right tail of the empirical distrubution function (edf) of the observations in DATA. Only observations lying in the interval [TAIL(1)-quantile of DATA,TAIL(2)-quantile of DATA] are used to obtain the least squares fit. CI_POWERTAIL(DATA,ALPHA,TAIL,CLT) allows to choose between the exact but slower to compute (binomial law based; CLT=0) and asymptotic (Gaussian law based; CLT=1, default) confidence intervals. CI_POWERTAIL(DATA,ALPHA,TAIL,CLT,1) plots the power law and the intervals in the current figure. Observations lying outside the curves spanned by the confidence intervals are likely to be (i.e. with probability 1-ALPHA) 'dragon kings', i.e. deviations from power law events (commonly known as 'black swans'). Note, that Taleb (2007) calls these 'tractable scientifically' events 'Mandelbrotian gray swans', to distinguish them from the 'totally intractable' black swans.

Suggested Citation

  • Joanna Janczura & Rafal Weron, 2012. "CI_POWERTAIL: MATLAB function to test for 'dragon kings' vs. 'black swans'," HSC Software M12001, Hugo Steinhaus Center, Wroclaw University of Technology.
  • Handle: RePEc:wuu:hscode:m12001

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    Blog mentions

    As found by, the blog aggregator for Economics research:
    1. The stock market and happiness
      by UDADISI in UDADISI on 2012-08-01 23:55:00


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    Cited by:

    1. Tonzer, Lena, 2017. "Uncertainty, financial crises, and subjective well-being," IWH Discussion Papers 2/2017, Halle Institute for Economic Research (IWH).
    2. Anita Ratcliffe & Karl Taylor, 2013. "Who Cares about Stock Market Booms and Busts? Evidence from Data on Mental Wellbeing," Working Papers 2012021, The University of Sheffield, Department of Economics.
    3. Frijters, Paul & Johnston, David W. & Shields, Michael A. & Sinha, Kompal, 2015. "A lifecycle perspective of stock market performance and wellbeing," Journal of Economic Behavior & Organization, Elsevier, vol. 112(C), pages 237-250.


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