Power laws, Pareto distributions and Zipf's law

By Mark Newman. 2005

5,824 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Statistical and Nonlinear Physics

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Citations in the corpus

Imbalanced Continual Learning with Partitioning Reservoir Sampling (2020, background): “This naturally occurring phenomenon is widely observed in vision and language datasets [70,63,80], with a whole other branch of machine learning that has focused solely on this topic.”
Graph evolution: Densification and shrinking diameters (2006, background): “In this case the Densification Power Law is the consequence of the fact that a power-law distribution with exponent γ < 2 has no finite expectation [41], and thus the average degree grows as degree exponent is constant.”
How Visibility and Divided Attention Constrain Social Contagion (2012, background): “This interpretation i s further strengthened by figure 5(a), where we see that highly connected users (250+ friends) are more likely to respond at short times and less likely to respond at long times, relativ e to low-connectivity users ( < 10 friends), yet the power-law exponent in the tails are ne”
A Spatio-Temporal Analysis Approach for Short-Term Forecast of Wind Farm Generation (2014, background): “, size of forest fires) that have strong componentwise correlations [20].”
Optical coherence tomography angiography (2017, background): “…earthquakes, material failure, transitions in shape memory metals, cancer metastasis, biologic evolution, traffic jam propagation, and epidemic transitions of disease (Bak, 1996; Hüfner and Mukhopadhyay, 1986; LukierskaWalasek and Topolski, 2014; Nagatani, 1998; Newman, 2005; Vives et al., 1994).”
Power-law distributions in binned empirical data (2012, methodology): “The regression methods yield relatively modest bias in ﬁtting to a logarithmically binned p.d.f. and a complementary c.d.f. [also called a “rank-frequency plot”—see Newman (2005)], which smooth out some of the noise in the upper tail.”
Repeat burglary victimisation: a tale of two theories (2008, background): “interest to see if, like many physical and social phenomenon (for a review see Newman 2005; see, also, Stevens 1957), the pattern of concentration followed a power-law distribution.”
The Return of the Policy That Shall Not Be Named: Principles of Industrial Policy (2019, background): “For the exponent found for the long horizon (50 years), the distribution is capable of producing black swans (see Newman et al. 2005).”
From criticality to final collapse: Evolution of the ''b-value" from 1.5 to 1.0 (2009, background): “A completely different demonstration that the condition of self-similarity (amax/L = constant on average) coupled with the condition of uniform damage in the body implies a = 3, comes from the treatment proposed by Newman [22], in which the scaling between amax and the number n of defects is obtaine”
On the probability of occurrence of extreme space weather events (2012, methodology): “Unless p(x) is computed from bins of data that are logarithmically spaced, the ever-smaller number of events landing in the largest event bins drives the errors associated with those estimates up [Newman, 2005].”
Languages cool as they expand: Allometric scaling and the decreasing need for new words (2012, background): “[29] Newman, M.”
Testing and recommending methods for fitting size spectra to data (2017, methodology): “…size-spectrum models ‘the number of individuals in each size group is often found to exhibit a powerlaw relationship with size’ (Andersen & Beyer 2006), and in empirical studies, fitting of straight lines on logarithmic axes implicitly implies the fitting of a power-law relationship (Newman 2005).”
Social media engagement: What motivates user participation and consumption on YouTube? (2017, background): “This type of distribution in terms of user participation on sites is known as the Pareto principle that suggests 80% of the work is done by 20% of individuals (Best & Neuhauser, 2006), which is also similar to the power law distribution in mathematics (Newman, 2005).”
Exploration in Interactive Personalized Music Recommendation: A Reinforcement Learning Approach (2013, background): “The distribution approximately follows the Zipf s law [Newman 2005], where only a small set of songs are repeated most of the time while all the rest are repeated much less often.”