# Power laws, Pareto distributions and Zipf's law

@article{Newman2005PowerLP, title={Power laws, Pareto distributions and Zipf's law}, author={Mark E. J. Newman}, journal={Contemporary Physics}, year={2005}, volume={46}, pages={323 - 351} }

When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distributions of the sizes of cities, earthquakes, forest fires, solar flares, moon craters and people's… Expand

#### Topics from this paper

#### 2,270 Citations

Power laws, Pareto distributions and Zipf's law

- Physics
- 2004

When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf’s law or the… Expand

The logarithmic Zipf law in a general urn problem

- Mathematics
- 2020

The origin of power-law behavior (also known variously as Zipf’s law) has been a topic of debate in the scientific community for more than a century. Power laws appear widely in physics, biology,… Expand

POWER-LAW DISTRIBUTIONS BASED ON EXPONENTIAL DISTRIBUTIONS: LATENT SCALING, SPURIOUS ZIPF'S LAW, AND FRACTAL RABBITS

- Mathematics, Physics
- 2015

The difference between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution.… Expand

Zipf's and Taylor's laws

- Mathematics, Physics
- 2018

Zipf's law states that the frequency of an observation with a given value is inversely proportional to the square of that value; Taylor's law, instead, describes the scaling between fluctuations in… Expand

Power-law and exponential rank distributions: A panoramic Gibbsian perspective

- Physics
- 2015

Abstract Rank distributions are collections of positive sizes ordered either increasingly or decreasingly. Many decreasing rank distributions, formed by the collective collaboration of human actions,… Expand

Universality of Zipf's law.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2010

It is shown that Zipf's law is, in fact, an inevitable outcome of a very general class of stochastic systems, based on the properties of the symbolic sequence obtained through successive observations over a system with an ubounded number of possible states. Expand

Pareto versus lognormal: a maximum entropy test.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2011

The results provide support for the theory that distributions with lognormal body and Pareto tail can be generated as mixtures of lognormally distributed units. Expand

Nonlinear Mechanisms of Generating Power Laws in Socioeconomic Systems

- Mathematics
- 2013

During the last decade, more and more systems studied in the social sciences were found to be described by power law statistical distributions. This class of distributions is fascinating for the… Expand

Power Law Distribution: Method of Multi-scale Inferential Statistics

- Mathematics
- 2012

Power law distribution appears in several scientific fields such as physics, earth science, economics, social science and many others. This paper illustrates new practical criteria for inferential… Expand

A review on the characterization of signals and systems by power law distributions

- Mathematics, Computer Science
- Signal Process.
- 2015

Twelve cases, namely worldwide technological accidents, the annual revenue of America's largest private companies, the number of inhabitants in America?s largest cities, the magnitude of earthquakes with minimum moment magnitude equal to 4, the total burned area in forest fires occurred in Portugal, and the net worth of the richer people in America are studied. Expand

#### References

SHOWING 1-10 OF 66 REFERENCES

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

- Computer Science, Mathematics
- Internet Math.
- 2003

A rich and long history is found of how lognormal distributions have arisen as a possible alternative to power law distributions across many fields, focusing on underlying generative models that lead to these distributions. Expand

A general theory of bibliometric and other cumulative advantage processes

- Mathematics, Computer Science
- J. Am. Soc. Inf. Sci.
- 1976

It is shown that such a stochastic law is governed by the Beta Function, containing only one free parameter, and this is approximated by a skew or hyperbolic distribution of the type that is widespread in bibliometrics and diverse social science phenomena. Expand

ON A CLASS OF SKEW DISTRIBUTION FUNCTIONS

- Mathematics
- 1955

It is the purpose of this paper to analyse a class of distribution functions that appears in a wide range of empirical data-particularly data describing sociological, biological and economic… Expand

From gene families and genera to incomes and internet file sizes: why power laws are so common in nature.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2002

If stochastic processes with exponential growth in expectation are killed (or observed) randomly, the distribution of the killed or observed state exhibits power-law behavior in one or both tails. Expand

Zipf's Law for Cities: An Explanation

- Economics
- 1999

Zipf ’s law is a very tight constraint on the class of admissible models of local growth. It says that for most countries the size distribution of cities strikingly fits a power law: the number of… Expand

Problems with fitting to the power-law distribution

- Mathematics, Physics
- 2004

Abstract.This short communication uses a simple experiment to show that fitting to a power law distribution by using graphical methods based on linear fit on the log-log scale is biased and… Expand

Random texts exhibit Zipf's-law-like word frequency distribution

- Mathematics, Computer Science
- IEEE Trans. Inf. Theory
- 1992

It is shown that the distribution of word frequencies for randomly generated texts is very similar to Zipf's law observed in natural languages such as English. The facts that the frequency of… Expand

Multiplicative processes and power laws

- Mathematics, Physics
- 1998

Takayasu, Sato, and Takayasu [Phys. Rev. Lett. 79, 966 (1997)] revisited the question of stochastic processes with multiplicative noise, which have been studied in several different contexts over the… Expand

Log-normal Distributions across the Sciences: Keys and Clues

- Biology
- 2001

Many widely used statistical methods, such as ANOVA (analysis of variance) and regression analysis, require that the data be normally distributed, but only rarely is the frequency distribution of data tested when these techniques are used. Expand

Power-law distribution of family names in Japanese societies

- Mathematics, Physics
- 2000

We study the frequency distribution of family names. From a common data base, we count the number of people who share the same family name. This is the size of the family. We find that (i) the total… Expand