| Author | Title | Year | Journal/Proceedings | Reftype | DOI/URL |
|---|---|---|---|---|---|
| Adamic, L. | Zipf, Power-laws, and Pareto -- a ranking tutorial [BibTeX] |
2002 | http://www.hpl.hp.com/research/idl/papers/ranking/ranking.html | misc | URL |
BibTeX:
@misc{adamic02tutorial,
author = {Adamic, Lada},
title = {Zipf, Power-laws, and Pareto -- a ranking tutorial },
year = {2002},
url = {http://www.hpl.hp.com/research/idl/papers/ranking/ranking.html}
}
|
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| Adamic, L.A. & Huberman, B.A. | Zipf's Law and the Internet [BibTeX] |
2002 | Glottometrics Vol. 3, pp. 143-150 |
article | |
BibTeX:
@article{adamic02zipf,
author = {Adamic, L. A. and Huberman, B. A.},
title = {Zipf's Law and the Internet},
journal = {Glottometrics},
year = {2002},
volume = {3},
pages = {143-150}
}
|
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| Newman, M.E.J. | The structure and function of complex networks [BibTeX] |
2003 | SIAM Review Vol. 45, pp. 167 |
article | URL |
BibTeX:
@article{newman03structure,
author = {Newman, M. E. J.},
title = {The structure and function of complex networks},
journal = {SIAM Review},
year = {2003},
volume = {45},
pages = {167},
url = {http://www.citebase.org/abstract?id=oai:arXiv.org:cond-mat/0303516}
}
|
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| Clauset, A., Shalizi, C.R. & Newman, M.E.J. | Power-law distributions in empirical data | 2007 | misc | DOI URL | |
| Abstract: Power-law distributions occur in many situations of scientific interest and ve significant consequences for our understanding of natural and man-made enomena. Unfortunately, the detection and characterization of power laws is mplicated by the large fluctuations that occur in the tail of the stribution -- the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power-law behavior lds. Commonly used methods for analyzing power-law data, such as ast-squares fitting, can produce substantially inaccurate estimates of rameters for power-law distributions, and even in cases where such methods turn accurate answers they are still unsatisfactory because they give no dication of whether the data obey a power law at all. Here we present a incipled statistical framework for discerning and quantifying power-law havior in empirical data. Our approach combines maximum-likelihood fitting thods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic d likelihood ratios. We evaluate the effectiveness of the approach with tests synthetic data and give critical comparisons to previous approaches. We also ply the proposed methods to twenty-four real-world data sets from a range of fferent disciplines, each of which has been conjectured to follow a power-law stribution. In some cases we find these conjectures to be consistent with the ta while in others the power law is ruled out. |
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BibTeX:
@misc{clauset2007powerlaw,
author = {Clauset, Aaron and Shalizi, Cosma Rohilla and Newman, M. E. J.},
title = {Power-law distributions in empirical data},
year = {2007},
note = {cite arxiv:0706.1062Comment: 43 pages, 11 figures, 7 tables, 4 appendices; code available at http://www.santafe.edu/~aaronc/powerlaws/},
url = {http://arxiv.org/abs/0706.1062},
doi = {http://dx.doi.org/10.1137/070710111}
}
|
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| Clauset, A., Shalizi, C.R. & Newman, M.E.J. | Power-Law Distributions in Empirical Data | 2009 | SIAM Review Vol. 51(4), pp. 661-703 |
article | DOI URL |
| 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 (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. | |||||
BibTeX:
@article{clauset2009powerlaw,
author = {Clauset, Aaron and Shalizi, Cosma Rohilla and Newman, M. E. J.},
title = {Power-Law Distributions in Empirical Data},
journal = {SIAM Review},
publisher = {SIAM},
year = {2009},
volume = {51},
number = {4},
pages = {661--703},
url = {http://link.aip.org/link/?SIR/51/661/1},
doi = {http://dx.doi.org/10.1137/070710111}
}
|
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| Newman, M.E.J. | Power laws, Pareto distributions and Zipf's law | 2004 | misc | URL | |
| Abstract: When the probability of measuring a particular value of some quantity varies versely as a power of that value, the quantity is said to follow a power law, so known variously as Zipf's law or the Pareto distribution. Power laws pear widely in physics, biology, earth and planetary sciences, economics and nance, computer science, demography and the social sciences. For instance, e distributions of the sizes of cities, earthquakes, solar flares, moon aters, wars and people's personal fortunes all appear to follow power laws. e origin of power-law behaviour has been a topic of debate in the scientific mmunity for more than a century. Here we review some of the empirical idence for the existence of power-law forms and the theories proposed to plain them. |
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BibTeX:
@misc{newman2004power,
author = {Newman, M. E. J.},
title = {Power laws, Pareto distributions and Zipf's law},
year = {2004},
url = {http://arxiv.org/abs/cond-mat/0412004}
}
|
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| Newman, M.E.J. | Power laws, Pareto distributions and Zipf's law [BibTeX] |
2005 | Contemporary Physics Vol. 46, pp. 323 |
article | URL |
BibTeX:
@article{newman05power,
author = {Newman, M. E. J.},
title = {Power laws, Pareto distributions and Zipf's law},
journal = {Contemporary Physics},
year = {2005},
volume = {46},
pages = {323},
url = {doi:10.1080/00107510500052444}
}
|
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| Stumme, G. | Iceberg Query Lattices for Datalog [BibTeX] |
2004 | Vol. 3127Conceptual Structures at Work: 12th International Conference on Conceptual Structures (ICCS 2004), pp. 109-125 |
inproceedings | URL |
BibTeX:
@inproceedings{stumme2004iceberg,
author = {Stumme, Gerd},
title = {Iceberg Query Lattices for Datalog},
booktitle = {Conceptual Structures at Work: 12th International Conference on Conceptual Structures (ICCS 2004)},
publisher = {Springer},
year = {2004},
volume = {3127},
pages = {109-125},
url = {http://www.kde.cs.uni-kassel.de/stumme/papers/2004/stumme2004iceberg.pdf}
}
|
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| Goldstein, M.L., Morris, S.A. & Yen, G.G. | Fitting to the power-law distribution | 2004 | The European Physical Journal B - Condensed Matter and Complex Systems Vol. 41(2), pp. 255-258 |
article | URL |
| Abstract: Version 1 of Goldstein 04 power law fit containing also the chi 2 test | |||||
BibTeX:
@article{Goldstein04powerlawfitV1,
author = {Goldstein, M. L. and Morris, S. A. and Yen, G. G.},
title = {Fitting to the power-law distribution},
journal = {The European Physical Journal B - Condensed Matter and Complex Systems},
year = {2004},
volume = {41},
number = {2},
pages = {255-258},
url = {http://arxiv.org/abs/cond-mat/0402322v1}
}
|
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| Barabási, A.-L. & Albert, R. | Emergence of scaling in random networks [BibTeX] |
1999 | Science Vol. 286, pp. 509-512 |
article | |
BibTeX:
@article{barabasi99emergence,
author = {Barabási, Albert-László and Albert, Réka},
title = {Emergence of scaling in random networks},
journal = {Science},
year = {1999},
volume = {286},
pages = {509--512}
}
|
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| Mitzenmacher, M. | A Brief History of Generative Models for Power Law and Lognormal Distributions | 2004 | Internet Mathematics Vol. 1(2), pp. 226-251 |
article | URL |
| Abstract: 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 ad 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. |
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BibTeX:
@article{mitzenmacher2004history,
author = {Mitzenmacher, M.},
title = {A Brief History of Generative Models for Power Law and Lognormal Distributions |
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