Pareto Distribution

Definition

Let $X$ be a random variable with outcome set $\mathbb{R}$ and PDF defined as

$$f_X(x)=\{\begin{array}{ll}\frac{\alpha x_{\mathrm{m}}^{\alpha }}{x^{\alpha +1}}& x\ge x_{\mathrm{m}},\\ 0& x<x_{\mathrm{m}}.\end{array}$$

where $x_m>0$ is the scale parameter which is the minimum possible value of $X$, and $\alpha >0$ is the shape parameter called as tail index.

References

Pareto distribution - Wikipedia