Fat tail

A fat-tailed distribution is a probability distribution that has the property, along with the other heavy-tailed distributions, that it exhibits large skewness or kurtosis. This comparison is often made relative to the normal distribution, or to the exponential distribution. Fat-tailed distributions have been empirically encountered in a variety of areas: economics, physics, and earth sciences. Some fat-tailed distributions have power law decay in the tail of the distribution, but they generally do not follow a power law everywhere.

The distribution of a random variable X is said to have a fat tail if

That is, if X has probability density function ${\displaystyle f_{X}(x)}$,

Here the tilde notation "${\displaystyle \sim }$" refers to the asymptotic equivalence of functions.

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