[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.