Sonstiges
Zipf, Power-laws, and Pareto - a ranking tutorial .
http://www.hpl.hp.com/research/idl/papers/ranking/ranking.html. 2002.
Lada Adamic.
[doi]
[BibTeX]
Artikel in Zeitschriften
Zipf's Law and the Internet.
Glottometrics, 3:143-150, 2002.
L. A. Adamic und B. A. Huberman.
[BibTeX]
The structure and function of complex networks.
SIAM Review, 45:167, 2003.
M. E. J. Newman.
[doi]
[BibTeX]
Sonstiges
Power-law distributions in empirical data.
2007. cite arxiv:0706.1062Comment: 43 pages, 11 figures, 7 tables, 4 appendices; code available at http://www.santafe.edu/~aaronc/powerlaws/.
Aaron Clauset, Cosma Rohilla Shalizi und M. E. J. Newman.
[doi]
[Kurzfassung]
[BibTeX]
Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution -- the part of the distribution representing large but rare events -- and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out.
Artikel in Zeitschriften
Power-Law Distributions in Empirical Data.
SIAM Review, 51(4):661-703, 2009.
Aaron Clauset, Cosma Rohilla Shalizi und M. E. J. Newman.
[doi]
[Kurzfassung]
[BibTeX]
Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution—the part of the distribution representing large but rare events—and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov–Smirnov (KS) statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data, while in others the power law is ruled out.
Sonstiges
Power laws, Pareto distributions and Zipf's law.
2004.
M. E. J. Newman.
[doi]
[Kurzfassung]
[BibTeX]
When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distributions of the sizes of cities, earthquakes, solar flares, moon craters, wars and people's personal fortunes all appear to follow power laws. The origin of power-law behaviour has been a topic of debate in the scientific community for more than a century. Here we review some of the empirical evidence for the existence of power-law forms and the theories proposed to explain them.
Artikel in Zeitschriften
Power laws, Pareto distributions and Zipf's law.
Contemporary Physics, 46:323, 2005.
M. E. J. Newman.
[doi]
[BibTeX]
Artikel in Tagungsbänden
Iceberg Query Lattices for Datalog.
In: K. E. Wolff, H. D. Pfeiffer und H. S. Delugach
(Herausgeber):
Conceptual Structures at Work: 12th International Conference on Conceptual Structures (ICCS 2004), Band 3127, Reihe LNCS, Seiten 109-125.
Springer, Heidelberg, 2004.
Gerd Stumme.
[doi]
[BibTeX]
Artikel in Zeitschriften
Fitting to the power-law distribution.
The European Physical Journal B - Condensed Matter and Complex Systems, 41(2):255-258, 2004.
M. L. Goldstein, S. A. Morris und G. G. Yen.
[doi]
[Kurzfassung]
[BibTeX]
Version 1 of Goldstein 04 power law fit containing also the chi 2 test
Emergence of scaling in random networks.
Science, 286:509-512, 1999.
Albert-László Barabási und Réka Albert.
[BibTeX]
A Brief History of Generative Models for Power Law and Lognormal Distributions.
Internet Mathematics, 1(2):226-251, 2004.
M. Mitzenmacher.
[doi]
[Kurzfassung]
[BibTeX]
Recently, I became interested in a current debate over whether file size distributions are best modelled by a power law distribution or a lognormal distribution. In trying to learn enough about these distributions to settle the question, I found a rich and long history, spanning many fields. Indeed, several recently proposed models from the computer science community have antecedents in work from decades ago. Here, I briefly survey some of this history, focusing on underlying generative models that lead to these distributions. One finding is that lognormal and power law distributions connect quite naturally, and hence, it is not surprising that lognormal distributions have arisen as a possible alternative to power law distributions across many fields.