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 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:
If the value of k is chosen judiciously then the Pareto distribution obeys the "8020 rule".
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