Power laws, Pareto distributions and Zipf's law.¶
Newman, M. (2005). Power laws, Pareto distributions and Zipf's law. Contemporary Physics, 46(5), 323-351.
Cited by¶
5 citations across 5 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Allometry and Scaling Law
- The distinction matters because allometry suggests an underlying principle (constraint, evolutionary pressure, physical law), whereas nonlinearity alone suggests only that the relationship is not linear.
This sourceReview establishing that polynomially (rather than exponentially) decaying tails recur across physics, biology, economics, and the social sciences, with a few extreme members dominating aggregates.
- The distinction matters because allometry suggests an underlying principle (constraint, evolutionary pressure, physical law), whereas nonlinearity alone suggests only that the relationship is not linear.
- Heavy-Tailed Distributions
- Heavy-tailedness encodes a structural pattern: slow tail decay → tail-dominated aggregates → unstable bulk statistics.
This sourceReview establishing that polynomially (rather than exponentially) decaying tails recur across physics, economics, biology, and the social sciences, with the few extreme members dominating aggregates (supporting D54-513, D54-514, D54-515, and the cross-domain knowledge transfer in D54-523).
SupportedVerified against the work's full text
Newman shows power-law tails are top-heavy, with essentially all of the total in the tail for low exponents, and that the mean then fluctuates wildly between samples.
“This implies that, while the mean may take a relatively small value on any particular repe- tition of the experiment, it must occasionally take a huge value”
- Heavy-tailedness encodes a structural pattern: slow tail decay → tail-dominated aggregates → unstable bulk statistics.
- Lindy Effect
- The age-proportional invariant is exact for a Pareto (power-law) lifetime distribution, which makes the formal case clean.
This sourceProperties of the Pareto/power-law distribution, including its survival function and tail exponent.
Supported in partVerified against the work's full text
Newman gives the Pareto survival function as a power law with exponent one less than the density exponent and a lower cutoff xmin; the paper's own exponent convention differs from the claim's.
“Thus the cumulative distribution function P (x) also fol- lows a power law, but with a different exponent α − 1, which is 1 less than the original exponent.”
- The age-proportional invariant is exact for a Pareto (power-law) lifetime distribution, which makes the formal case clean.
- Pareto Effect (80/20 Rule)
- Subsequent research documented Pareto-like distributions in income (Piketty-Saez top-income shares), firm size (Gibrat's law with Pareto-tail extensions), city population, and household wealth
This sourceReview establishing that polynomially (rather than exponentially) decaying tails recur across physics, economics, biology, and the social sciences, with the few extreme members dominating aggregates (supporting D54-513, D54-514, D54-515, and the cross-domain knowledge transfer in D54-523).
- Subsequent research documented Pareto-like distributions in income (Piketty-Saez top-income shares), firm size (Gibrat's law with Pareto-tail extensions), city population, and household wealth
- Scale Invariance
- A statistical distribution P(X > x) ∝ x^(−α) for large x exhibits scale invariance of its tail
This sourceReview establishing that polynomially (rather than exponentially) decaying tails recur across physics, economics, biology, and the social sciences, with the few extreme members dominating aggregates (supporting D54-513, D54-514, D54-515, and the cross-domain knowledge transfer in D54-523).
SupportedVerified against the work's full text
Newman shows that power laws are the only scale-free distributions, keeping their shape under rescaling, and that a power-law cumulative tail P(x) has exponent alpha-1.
“A power-law distribution is also sometimes called a scale-free distribution. Why? Because a power law is the only distribution that is the same whatever scale we look”
- A statistical distribution P(X > x) ∝ x^(−α) for large x exhibits scale invariance of its tail
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 3 of 5 citations: 2 supported, 1 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
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