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Fitting long‐tailed distribution to empirical data
Author(s) -
Gil Joseph Yossi,
Monni Cristina
Publication year - 2017
Publication title -
concurrency and computation: practice and experience
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.309
H-Index - 67
eISSN - 1532-0634
pISSN - 1532-0626
DOI - 10.1002/cpe.4223
Subject(s) - weibull distribution , empirical distribution function , variety (cybernetics) , power law , distribution (mathematics) , mathematics , algorithm , iterated function , computer science , statistics , mathematical analysis
Summary 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 χ 2 test performs better than the other. Our algorithm is general and can be applied to any numerical dataset.