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:
If the value of k is chosen judiciously then the Pareto distribution obeys the "80-20 rule".
See also:
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where x is any number greater than xmin, 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, xmin and k.