The Pareto, Zipf and other power laws

By W. Reed. 2001

653 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

Citations in the corpus

Large-Scale Long-Tailed Recognition in an Open World (2019, background): “Our visual world is inherently long-tailed and openended: The frequency distribution of visual categories in our daily life is long-tailed [38], with a few common classes and many more rare classes, and we constantly encounter new visual concepts as we navigate in an open world.”
Balanced Knowledge Distillation for Long-tailed Learning (2021, background): “However, in practical scenarios, data tends to exhibit long-tailed distribution [38, 17], wherein a few classes (head classes) have a significantly larger number of instances than other classes (tail classes).”
A Unified Theory of Firm Selection and Growth (2009, neutral): “ Reed (2001) provides another proof using moment generating functions in which the intuition is also somewhat limited.”
Is Label Smoothing Truly Incompatible with Knowledge Distillation: An Empirical Study (2021, methodology): “The training set of this dataset is constructed by a Pareto distribution (Reed, 2001) with a power value α = 6.”
Welfare and Trade without Pareto (2014, background): “This demonstration that Gibrat’s Law implies a limiting distribution that is log-normal echoes similar arguments by Sutton (1997) for firms and Eeckhout (2004) for cities.”
Statistical Size Distributions in Economics and Actuarial Sciences (2003, background): “This yields an unconditional distribution to which Reed (2001b) referred as the double-Pareto-lognormal distribution.”
The Matthew effect in empirical data (2014, background): “We also discuss whether the Matthew effect is due to chance or optimisation, for example related to homophily in social systems or efficacy in technological systems, and we outline possible directions for future research.”
Flickr tag recommendation based on collective knowledge (2008, background): “Beijing, China 10 100 1000 10000 100000 1e+06 1 10 100 1000 10000 100000 tag frequency tag Figure 1: Distribution of the Tag Frequency in Flickr. by a power law [19] [1], and the probability of a tag having tag frequency x is proportional to x −1.15 .”
Long-Tailed Classification by Keeping the Good and Removing the Bad Momentum Causal Effect (2020, neutral): “However, the cost of expanding them to a larger class vocabulary with balanced data is not linear — but exponential — as the data will be inevitably long-tailed by Zipf’s law [6].”
Zipf's law for cities: a cross-country investigation (2005, neutral): “Our sample of 75 countries includes all the countries in the Rosen and Resnick sample, except for Ghana, Sri Lanka and Zaire. Some discussion of the sample selection criteria used here is in order. Cheshire (1999) raises this issue. He argues that there are three possible criteria: a fixed number of”
Models of Growth and Firm Heterogeneity (2010, neutral): “[63] Reed, W.”
Investigating the Exponential Age Distribution of Firms (2010, methodology): “…over an exponential distribution to obtain a Pareto) was previously used by Huberman and Adamic (1999) to explain the number of web pages on internet sites, before being brought into economics by Reed (2001), who focused mainly on explaining the distributions of earnings and city sizes.”