 When this distribution is used to model the distribution of wealth, then the parameter "α" is called the Pareto index.From the definition, the cumulative distribution function of a Pareto random variable with parameters "α" and "x"m is

It follows (by differentiation) that the probability density function is

When plotted on linear axes, the distribution assumes the familiar J-shaped curve which approaches each of the orthogonal axes asymptotically.All segments of the curve are self-similar (subject to appropriate scaling factors).