@article{brzezinski2015power,
  abstract = {Modeling distributions of citations to scientific papers is crucial for understanding how science develops. However, there is a considerable empirical controversy on which statistical model fits the citation distributions best. This paper is concerned with rigorous empirical detection of power-law behaviour in the distribution of citations received by the most highly cited scientific papers. We have used a large, novel data set on citations to scientific papers published between 1998 and 2002 drawn from Scopus. The power-law model is compared with a number of alternative models using a likelihood ratio test. We have found that the power-law hypothesis is rejected for around half of the Scopus fields of science. For these fields of science, the Yule, power-law with exponential cut-off and log-normal distributions seem to fit the data better than the pure power-law model. On the other hand, when the power-law hypothesis is not rejected, it is usually empirically indistinguishable from most of the alternative models. The pure power-law model seems to be the best model only for the most highly cited papers in “Physics and Astronomy”. Overall, our results seem to support theories implying that the most highly cited scientific papers follow the Yule, power-law with exponential cut-off or log-normal distribution. Our findings suggest also that power laws in citation distributions, when present, account only for a very small fraction of the published papers (less than 1 % for most of science fields) and that the power-law scaling parameter (exponent) is substantially higher (from around 3.2 to around 4.7) than found in the older literature.},
  author = {Brzezinski, Michal},
  doi = {10.1007/s11192-014-1524-z},
  interhash = {b162eddb3ff76a9eef5daf450da934c0},
  intrahash = {8ef9a6fbfcca3d599ca500cf4f9a2e39},
  issn = {0138-9130},
  journal = {Scientometrics},
  language = {English},
  number = 1,
  pages = {213-228},
  publisher = {Springer Netherlands},
  title = {Power laws in citation distributions: evidence from Scopus},
  url = {http://dx.doi.org/10.1007/s11192-014-1524-z},
  volume = 103,
  year = 2015
}

@article{clauset2009powerlaw,
  author = {Clauset, Aaron and Shalizi, Cosma Rohilla and Newman, M. E. J.},
  doi = {10.1137/070710111},
  eprint = {http://dx.doi.org/10.1137/070710111},
  interhash = {9ce8658af5a6358a758bfdb819f73394},
  intrahash = {c0097d202655474b1db6811ddea03410},
  journal = {SIAM Review},
  number = 4,
  pages = {661-703},
  title = {Power-Law Distributions in Empirical Data},
  url = {/brokenurl#         http://dx.doi.org/10.1137/070710111    },
  volume = 51,
  year = 2009
}

@misc{alstott2013powerlaw,
  abstract = {Power laws are theoretically interesting probability distributions that are
also frequently used to describe empirical data. In recent years effective
statistical methods for fitting power laws have been developed, but appropriate
use of these techniques requires significant programming and statistical
insight. In order to greatly decrease the barriers to using good statistical
methods for fitting power law distributions, we developed the powerlaw Python
package. This software package provides easy commands for basic fitting and
statistical analysis of distributions. Notably, it also seeks to support a
variety of user needs by being exhaustive in the options available to the user.
The source code is publicly available and easily extensible.},
  author = {Alstott, Jeff and Bullmore, Ed and Plenz, Dietmar},
  doi = {10.1371/journal.pone.0085777},
  interhash = {3e00fb5f61ea9069884122a61ca60c1f},
  intrahash = {5c2f8406c2fca10773f28e538fbc115d},
  note = {cite arxiv:1305.0215Comment: 18 pages, 6 figures, code and supporting information at  https://github.com/jeffalstott/powerlaw and  https://pypi.python.org/pypi/powerlaw},
  title = {Powerlaw: a Python package for analysis of heavy-tailed distributions},
  url = {http://arxiv.org/abs/1305.0215},
  year = 2013
}

@misc{Clauset2007,
  abstract = {  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.
},
  author = {Clauset, Aaron and Shalizi, Cosma Rohilla and Newman, M. E. J.},
  interhash = {2e3bc5bbd7449589e8bfb580e8936d4b},
  intrahash = {7da1624e601898dd74df839ce2daeb24},
  note = {cite arxiv:0706.1062
Comment: 43 pages, 11 figures, 7 tables, 4 appendices; code available at
  http://www.santafe.edu/~aaronc/powerlaws/},
  title = {Power-law distributions in empirical data},
  url = {http://arxiv.org/abs/0706.1062},
  year = 2007
}