Fat tail

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The accursed part of your probability distribution, where you discover it diverges from the normal distribution lazily factored into all your models.

In probability theory, “kurtosis” (from Greek: κυρτός, meaning “curved”) is the measure of the fatness of the tails of a distribution of variables. Higher kurtosis corresponds to greater deviation from the mean — more outliers — and is less interested in the shape of the distribution close to the mean.

As Nassim Nicholas Taleb notes in his fantastically bombastic The Black Swan: The Impact of the Highly Improbable, many a trading desk has come unstuck by mistaking the similarity of the hump of a leptokurtic curve — the bit near the middle — to a normal distribution, because there haven't collected any data at the extremes.

A normal distribution has a kurtosis of 3.

Leptokurtic distributions are from Mars, platykurtic distributions are from Venus

Platykurtic distributions: mediocristan: Distributions with lower kurtosis than 3 are “platykurtic”, and will produce fewer outliers than a normal distribution. For example, a uniform distribution — eg a coin toss, or a deck of cards — which does not produce outliers art all. You can’t get an 11 of hearts.

Leptokurtic distributions: exrtremistan: Distributions with greater kurtosis than 3 are “leptokurtic”. The tails of a leptokurtic distribution will be fatter — they will tend to zero more slowly than those of a normal distribution, and there will be more outliers.

See also