The Pareto distribution named after the Italian economist Vilfredo Pareto is a power law distribution found in a large number of real-world situations.
If X is a random variable with a Pareto distribution, then the probability distribution of X is characterized by the statement
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 xmin k/(k-1) (if k=1, the expected value doesn't exist) and its standard deviation is xmin / (k-1) √(k/(k-2)) (for k=1 or 2 the standard deviation doesn't exist).
Examples of Pareto distributions:
- wealth distribution in individuals before 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
- add other examples of Pareto distributions here
See also:
External links:- William J. Reed: The Pareto, Zipf and other power laws, http://linkage.rockefeller.edu/wli/zipf/reed01_el.pdf