## The Pareto Distribution

The probability density function of a Pareto distribution is

This is shown below forand various values of

The cumulative distribution function is then found by integration:forand 0 otherwise.

- The mean and variance areforandfor 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.