Pareto distribution Guide, Meaning , Facts, Information and Description

The Pareto distribution named after the Italian economist Vilfredo Pareto is a power law distribution found in a large number of real-world situations. This distribution is also known, mostly outside economics, as the Bradford distribution.

If X is a random variable with a Pareto distribution, then the probability distribution of X is characterized by the statement

where x is any number greater than x_min, which is the (necessarily positive) minimum possible value of X, and k is a positive parameter. The family of Pareto distributions is parameterized by two quantities, x_min and k. The density is then

Pareto distributions are continuous probability distributions. "Zipf's law", also sometimes called the "zeta distribution", may be thought of as a discrete counterpart of the Pareto distribution. The expected value of a random variable following a Pareto distribution is

(if , the expected value is infinite) and its standard deviation is  (if , the standard deviation doesn't exist).

Examples said to be approximately Pareto distributions:

• wealth distribution in individuals before modern industrial capitalism created the vast middle class
• wealth distribution in individuals even after modern industrial capitalism created the vast middle class
• sizes of human settlements
• visits to Wikipedia pages
• clusters of Bose-Einstein condensate near absolute zero
• file size distribution of Internet traffic which uses the TCP protocol
• value of oil reserves in oil fields
• the number of fatalities due to hurricanes?

See also

• Pareto principle
• Pareto interpolation

External links

• William J. Reed: The Pareto, Zipf and other power laws, http://linkage.rockefeller.edu/wli/zipf/reed01_el.pdf

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