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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. | {{a|statistics|}}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 [[outlier]]s — and is less interested in the shape of the distribution close to the mean. | 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 [[outlier]]s — and is less interested in the shape of the distribution close to the mean. | ||
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===Leptokurtic distributions are from Mars, platykurtic distributions are from Venus=== | ===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: Extremistan''': 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. | ||
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*[[Lentil convexity]] | |||
Latest revision as of 09:14, 26 June 2024
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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: Extremistan: 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.