The probability density function of a Pareto distribution is
This is shown below for
and various values of
The cumulative distribution function is then found by integration:
for
and 0 otherwise.
- The mean and variance are
for
and
for
respectively.
Example: The Pareto distribution may be used to model the distribution of wealth and income with x-m the minimum wage or state benefit level, the sizes of human settlements, oil fields etc.