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

By Michael M. Mitzenmacher. 2004

1,865 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Networks and Communications

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Citations in the corpus

Graphite: Iterative Generative Modeling of Graphs (2018, background): “We direct the interested reader to prominent surveys on this topic [32, 31, 5].”
Complexity and Empirical Economics (2005, background): “…normal distribution, which would mean the log probability density of the process is log fxðcÞ ¼ log c log ffiffiffiffiffi 2p p rx ½log c EðxÞ 2 2r2x : ð6Þ As Mitzenmacher (2003) observes, one can rewrite this expression as log fxðcÞ ¼ log cð Þ2 2r2x þ EðxÞ r2x 1 log c log ffiffiffiffiffi 2p p rx…”
Concentration Inequalities and Martingale Inequalities: A Survey (2006, background): “Before we proceed, we first give a short description for the preferential attachment scheme [3, 21]: • With probability p, for some fixed p, add a new vertex v, and add an edge {u, v} from v by randomly and independently choosing u in proportion to the degree of u in the current graph.”
A versatile and accurate approximation for LRU cache performance (2012, background): “The reason why content popularity follows the Zipf law remains unclear though the discussion by Mitzenmacher on generative models for power laws provides some possible explanations [15].”
powerlaw: A Python Package for Analysis of Heavy-Tailed Distributions (2013, background): “However, diﬃculties in distinguishing the power law from the lognormal are common and well-described, and similar issues apply to the stretched exponential and other heavy-tailed distributions [11–13].”
Just two moments! A cautionary note against use of high-order moments in multifractal models in hydrology (2013, background): “Despite all its moments being theoretically finite, the log-normal distribution is very similar in shape to a power-type distribution (Pareto), in the sense that the two distributions appear almost indistinguishable from each other for a large portion of their body (Mitzenmacher, 2004).”
A framework for Bayesian optimality of psychophysical laws (2012, background): “Indeed, lognormal and power-law distributions are often empirically indistinguishable (Mitzenmacher, 2004).”
Skewed Wealth Distributions: Theory and Empirics (2018, positive): “32A particularly simple solution can be obtained with simplfying assumptions, following Mitzenmacher (2004), pp.”
Statistical analysis of the social network and discussion threads in slashdot (2008, methodology): “To find a functional form which best explains the observed data, we compare two approximations: the “usually assumed” power-law (PL) hypothesis, and a truncated lognormal (LN) hypothesis [16].”
Growth of the flickr social network (2008, methodology): “For a more detailed treatment of these and other models, we refer the reader to Mitzenmacher [14].”
Balanced allocations: the weighted case (2007, neutral): “STOC 07, June 11 13, 2007, San Diego, California, USA.”
Cumulative Advantage as a Mechanism for Inequality: A Review of Theoretical and Empirical Developments (2006, background): “Newman further points out that strict CA (which we formalize below) is one mechanism by which a power-law distribution is produced, but other mechanisms can also produce power-law distributions (see Mitzenmacher 2003 for a discussion of the related literature based on the lognormal distribution).”