Power law - Definition and Overview

In physics, a power law relationship between two scalar quantities x and y is any such that the relationship can be written as

<math>y = ax^k\,\!<math>

where a (the constant of proportionality) and k (the exponent of the power law) are constants.

Examples of power law relationships:

• The Stefan-Boltzmann law
• The inverse-square law of Newtonian gravity
• Gamma correction relating light intensity with voltage

Examples of power law probability distributions:

• Pareto distribution
• Zipf's law

Power laws are among the most frequent scaling laws that describe the scaling invariance found in many natural phenomena.

External links

• Zipf, Power-laws, and Pareto - a ranking tutorial (http://www.hpl.hp.com/research/idl/papers/ranking/ranking.html)
• A claim that the blogosphere obeys a powerlaw distribution (http://www.shirky.com/writings/powerlaw_weblog.html)
• Zipf Law, Zipf Distribution: An Introduction (http://www.cs.unc.edu/~vivek/home/stenopedia/zipf/)