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).
- 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.
- 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).
- A statistical distribution P(X > x) ∝ x^(−α) for large x exhibits scale invariance of its tail
Verification¶
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