A Brief History of Generative Models for Power Law and Lognormal Distributions

@article{Mitzenmacher2003ABH,
  title={A Brief History of Generative Models for Power Law and Lognormal Distributions},
  author={M. Mitzenmacher},
  journal={Internet Mathematics},
  year={2003},
  volume={1},
  pages={226 - 251}
}
  • M. Mitzenmacher
  • Published 2003
  • Mathematics, Computer Science
  • Internet Mathematics
  • 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… CONTINUE READING
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    References

    SHOWING 1-10 OF 172 REFERENCES
    The Double Pareto-Lognormal Distribution—A New Parametric Model for Size Distributions
    • 380
    • Highly Influential
    • PDF
    On 1/f noise and other distributions with long tails.
    • E. Montroll, M. Shlesinger
    • Medicine, Mathematics
    • Proceedings of the National Academy of Sciences of the United States of America
    • 1982
    • 312
    • PDF
    Some Further Notes on a Class of Skew Distribution Functions
    • H. Simon
    • Mathematics, Computer Science
    • Inf. Control.
    • 1960
    • 114
    Population fluctuations, power laws and mixtures of lognormal distributions
    • 89
    Maximum entropy formalism, fractals, scaling phenomena, and 1/f noise: A tale of tails
    • 260
    From gene families and genera to incomes and internet file sizes: why power laws are so common in nature.
    • W. Reed, B. Hughes
    • Mathematics, Medicine
    • Physical review. E, Statistical, nonlinear, and soft matter physics
    • 2002
    • 192
    • PDF
    On the tails of web file size distributions
    • 60
    • PDF
    ON A CLASS OF SKEW DISTRIBUTION FUNCTIONS
    • 2,331
    Informetric distributions, part I: Unified overview
    • 40
    Informetric distributions, part I: Unified overview
    • 53
    • PDF