{
  "id": "cond-mat/0402322",
  "version": "v3",
  "published": "2004-02-11T22:44:34.000Z",
  "updated": "2004-08-13T22:20:27.000Z",
  "title": "Problems with Fitting to the Power-Law Distribution",
  "authors": [
    "Michel L. Goldstein",
    "Steven A. Morris",
    "Gary G. Yen"
  ],
  "comment": "4 pages, 1 figure, 2 tables",
  "doi": "10.1140/epjb/e2004-00316-5",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn",
    "cond-mat.other"
  ],
  "abstract": "This short communication uses a simple experiment to show that fitting to a power law distribution by using graphical methods based on linear fit on the log-log scale is biased and inaccurate. It shows that using maximum likelihood estimation (MLE) is far more robust. Finally, it presents a new table for performing the Kolmogorov-Smirnof test for goodness-of-fit tailored to power-law distributions in which the power-law exponent is estimated using MLE. The techniques presented here will advance the application of complex network theory by allowing reliable estimation of power-law models from data and further allowing quantitative assessment of goodness-of-fit of proposed power-law models to empirical data.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-08-13T22:20:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "power-law distribution",
      "power-law models",
      "power law distribution",
      "maximum likelihood estimation",
      "complex network theory"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}