@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
}

@article{vuong1989likelihood,
  abstract = {In this paper, we develop a classical approach to model selection. Using the Kullback-Leibler Information Criterion to measure the closeness of a model to the truth, we propose simple likelihood-ratio based statistics for testing the null hypothesis that the competing models are equally close to the true data generating process against the alternative hypothesis that one model is closer. The tests are directional and are derived successively for the cases where the competing models are non-nested, overlapping, or nested and whether both, one, or neither is misspecified. As a prerequisite, we fully characterize the asymptotic distribution of the likelihood ratio statistic under the most general conditions. We show that it is a weighted sum of chi-square distribution or a normal distribution depending on whether the distributions in the competing models closest to the truth are observationally identical. We also propose a test of this latter condition.},
  author = {Vuong, Quang H.},
  copyright = {Copyright © 1989 The Econometric Society},
  interhash = {e00a4353cb1b1241e5d3c52f531be8bd},
  intrahash = {6888912f6666d4de22bdc794a05dfa1b},
  issn = {00129682},
  journal = {Econometrica},
  jstor_articletype = {research-article},
  jstor_formatteddate = {Mar., 1989},
  language = {English},
  number = 2,
  pages = {pp. 307-333},
  publisher = {The Econometric Society},
  title = {Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses},
  url = {http://www.jstor.org/stable/1912557},
  volume = 57,
  year = 1989
}

@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
}