202601121628
Status: #reference
Tags: Financial Machine Learning, Statistics
State: #nascient

Pareto Distribution

Saw it in a few classes, but created this note since it was mentioned in Advances in Financial Machine Learning by Prado and that made me realize this distribution wasn't fortuitous.

The Pareto distribution is the antithesis of the Normal Distribution which is used when we are dealing with things that compounds (money, bacterias, etc.) rather than averages. While the latter is based on the Central Limit Theorem, the former follows the Power Laws. (Additive vs Multiplicative processes)

One of the things that make it especially relevant in financial statistics is the non-nihility of the fat-tail risk. Better formulated, it assigns a significant density to "unlikely" events. The kurtosis of the Pareto (and Financial Markets) is said to be leptokurtic, which means that the while the peak is higher, the tails are fatter (It has a Pearson Kurtosis > 3).

This modeling is more realistic when it comes to model things like Blackswan Events and other statistically unlikely things that happen all the times. A bot or strategy based on a Gaussian distribution is solvent until it is not, since it thinks events many standard deviations are virtually impossible; one based on a Pareto distribution should be able to account for those "rare" events.

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