Fat-tailed distribution

The class of fat-tailed distributions includes those whose tails decay like a power law, which is a common point of reference in their use in the scientific literature.

the claim of a fat tail is more ambiguous, because in this parameter range, the variance, skewness, and kurtosis can be finite, depending on the precise value of

As a consequence, when data arise from an underlying fat-tailed distribution, shoehorning in the "normal distribution" model of risk—and estimating sigma based (necessarily) on a finite sample size—would understate the true degree of predictive difficulty (and of risk).

[6] In finance, fat tails often occur but are considered undesirable because of the additional risk they imply.

For example, an investment strategy may have an expected return, after one year, that is five times its standard deviation.

Assuming a normal distribution, the likelihood of its failure (negative return) is less than one in a million; in practice, it may be higher.

However, traumatic "real-world" events (such as an oil shock, a large corporate bankruptcy, or an abrupt change in a political situation) are usually not mathematically well-behaved.

In marketing, the familiar 80-20 rule frequently found (e.g. "20% of customers account for 80% of the revenue") is a manifestation of a fat tail distribution underlying the data.

The probability density function for logarithm of weekly record sales changes is highly leptokurtic and characterized by a narrower and larger maximum, and by a fatter tail than in the normal distribution case.

On the other hand, this distribution has only one fat tail associated with an increase in sales due to promotion of the new records that enter the charts.