Pareto distribution
The
Pareto distribution named after the Italian
economist Vilfredo Pareto is a
power law distribution found in a large number of realworld situations.
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.
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 x_{min} k/(k1) (if k=1, the expected value doesn't exist) and its standard deviation is x_{min} / (k1) √(k/(k2)) (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 BoseEinstein condensate near absolute zero
 file size distribution of Internet traffic which uses the TCP protocol
 add other examples of Pareto distributions here
If the value of
k is chosen judiciously then the Pareto distribution obeys the
"8020 rule.
See also:
External links: