Many authors use the term Pareto-Levy distribution, though Im not clear how these are different from Pareto. Are these also Power Law distributions and is there a way of visually confirming if an empirical distribution is likely Pareto Levy?



Difference between Pareto-Levy and Pareto distributions
The name "Pareto-Lévy" law was coined by Mandelbrot in [The Pareto-Lévy Law and the Distribution of Income](http://www.jstor.org/stable/2525289?seq=1#page_scan_tab_contents), and introduced to correct for the deficiency of the Pareto income distribution at low incomes. It is a [stable distribution](https://en.wikipedia.org/wiki/Stable_distribution) with stability parameter $\alpha\in(1,2)$, and therefore distinct from the [Lévy distribution](https://en.wikipedia.org/wiki/L%C3%A9vy_distribution), which has $\alpha=1/2$. The Pareto-Lévy distribution has the power-law tail of the [Pareto distribution](https://en.wikipedia.org/wiki/Pareto_distribution) at large values of the random variable, but differs at small values.


