CI_WEIBULLTAIL: MATLAB function to test for 'dragon kings' in Weibull-type tails

Joanna Janczura and Rafał Weron

HSC Software from Hugo Steinhaus Center, Wroclaw University of Science and Technology

Abstract: [CI_LO,CI_HI]=CI_WEIBULLTAIL(DATA,ALPHA,TAIL) calculates confidence intervals of significance level ALPHA for a Weibull law (i.e. a stretched exponential 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_WEIBULLTAIL(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_WEIBULLTAIL(DATA,ALPHA,TAIL,CLT,1) plots the Weibull 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 Weibull law.

Language: MATLAB
Requires: MATLAB (tested on MATLAB ver. 7.9).
Keywords: Black swan; Dragon king; Weibull law; Stretched exponential law; Empirical distribution function; Confidence interval. (search for similar items in EconPapers)
Date: 2012-03-03
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Downloads: (external link)
http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/hscode/ci_weibulltail_old.m Program file (older versions of Matlab) (text/plain)
http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/hscode/ci_weibulltail.m Program file (Matlab 2016 and newer) (text/plain)

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