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Volume 61, Issue 6 (Dec 2013)

Issues

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

Anna Deluca
  • Centre de Recerca Matemàtica, Edifici C, Bellaterra, Barcelona, Spain
  • Departament de Matemàtiques, Universitat Autònoma de Barcelona, Cerdanyola, Spain
  • Email:
/ Álvaro Corral
  • Centre de Recerca Matemàtica, Edifici C, Bellaterra, Barcelona, Spain
  • Departament de Matemàtiques, Universitat Autònoma de Barcelona, Cerdanyola, Spain
  • Email:
Published Online: 2013-09-26 | DOI: https://doi.org/10.2478/s11600-013-0154-9

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.

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

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Published Online: 2013-09-26

Published in Print: 2013-12-01


Citation Information: Acta Geophysica, ISSN (Online) 1895-7455, ISSN (Print) 1895-6572, DOI: https://doi.org/10.2478/s11600-013-0154-9. Export Citation

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Journal of Geophysical Research: Solid Earth, 2015, Page n/a
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Naresh Devineni, Upmanu Lall, Chen Xi, and Philip Ward
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2015, Volume 25, Number 7, Page 075407
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Francesc Font-Clos and Álvaro Corral
Physical Review Letters, 2015, Volume 114, Number 23
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Francesc Font-Clos, Gunnar Pruessner, Nicholas R Moloney, and Anna Deluca
New Journal of Physics, 2015, Volume 17, Number 4, Page 043066
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Álvaro Corral
Chaos, Solitons & Fractals, 2015, Volume 74, Page 99
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B. Gomez, A. Corral, A. R. Orpin, M. J. Page, H. Pouderoux, and P. Upton
Geology, 2015, Volume 43, Number 2, Page 103
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Vladimir Filimonov and Didier Sornette
Chaos, Solitons & Fractals, 2015, Volume 74, Page 27

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