Fitting and goodness-of-fit test of non-truncated and truncated power-law distributions

Anna Deluca, Álvaro Corral

    Research output: Contribution to journalArticleResearchpeer-review

    64 Citations (Scopus)

    Abstract

    Recently, Clauset, Shalizi, and Newman have proposed a systematic method to find over which range (if any) a certain distribution behaves as a power law. However, their method has been found to fail, in the sense that true (simulated) power-law tails are not recognized as such in some instances, and then the power-law hypothesis is rejected. Moreover, the method does not work well when extended to power-law distributions with an upper truncation. We explain in detail a similar but alternative procedure, valid for truncated as well as for non-truncated power-law distributions, based in maximum likelihood estimation, the Kolmogorov-Smirnov goodness-of-fit test, and Monte Carlo simulations. An overview of the main concepts as well as a recipe for their practical implementation is provided. The performance of our method is put to test on several empirical data which were previously analyzed with less systematic approaches. We find the functioning of the method very satisfactory. © 2013 Versita Warsaw and Springer-Verlag Wien.
    Original languageEnglish
    Pages (from-to)1351-1394
    JournalActa Geophysica
    Volume61
    Issue number6
    DOIs
    Publication statusPublished - 1 Dec 2013

    Keywords

    • binning
    • goodness-of-fit tests
    • power-law distribution estimation
    • seismic-moment distribution
    • tropicalcyclone energy
    • waiting-time distribution

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