On estimating the exponent of power-law frequency distributions

Ethan P. White, Brian J. Enquist, Jessica L. Green

Research output: Contribution to journalArticle

229 Scopus citations

Abstract

Power-law frequency distributions characterize a wide array of natural phenomena. In ecology, biology, and many physical and social sciences, the exponents of these power laws are estimated to draw inference about the processes underlying the phenomenon, to test theoretical models, and to scale up from local observations to global patterns. Therefore, it is essential that these exponents be estimated accurately. Unfortunately, the binning-based methods traditionally used in ecology and other disciplines perform quite poorly. Here we discuss more sophisticated methods for fitting these exponents based on cumulative distribution functions and maximum likelihood estimation. We illustrate their superior performance at estimating known exponents and provide details on how and when ecologists should use them. Our results confirm that maximum likelihood estimation outperforms other methods in both accuracy and precision. Because of the use of biased statistical methods for estimating the exponent, the conclusions of several recently published papers should be revisited.

Original languageEnglish (US)
Pages (from-to)905-912
Number of pages8
JournalEcology
Volume89
Issue number4
DOIs
StatePublished - Apr 1 2008

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Keywords

  • Binning
  • Distribution
  • Exponent
  • Maximum likelihood estimation
  • Power laws

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics

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