Fitting long-tailed distribution to empirical data.

Power laws can fit a variety of distributions coming from real data, so a systematic approach to the measurement of the accuracy of fitting algorithms is essential. We discuss the limits of the analysis of empirical fat-tailed distributions, which can describe a variety of evolving systems, both natural and man-made. An algorithm to fit fat-tailed distributions is presented and tested against samplings of the power law, the Yule, the log-normal, and Weibull distributions. We compute the parameters defining the shape of each distribution and test the results against simulations. We compare our method with another state-of-the-art technique to estimate the parameters of empirical distributions. The accuracy of the estimations is discussed, and we conclude that our method based on a weighted iterated(2) test performs better than the other. Our algorithm is general and can be applied to any numerical dataset.