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?
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The name "Pareto-Lévy" law was coined by Mandelbrot in The Pareto-Lévy Law and the Distribution of Income, and introduced to correct for the deficiency of the Pareto income distribution at low incomes. It is a stable distribution with stability parameter $\alpha\in(1,2)$, and therefore distinct from the Lévy distribution, which has $\alpha=1/2$. The Pareto-Lévy distribution has the power-law tail of the Pareto distribution at large values of the random variable, but differs at small values.
answered Jul 11, 2016 at 6:39
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$\begingroup$ Is there any way to graphically confirm a Pareto-Levy distribution? My empirical data has a heavy right tail which falls on a straight line (log-log scale) $\endgroup$– BoomboiCommented Jul 11, 2016 at 12:01
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$\begingroup$ this is a fitting procedure, explained for example here $\endgroup$ Commented Jul 11, 2016 at 13:03