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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?

1 See also

2 External links

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

Probability distributions

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