Fat-tailed distribution

A fat-tailed distribution is a probability distribution that exhibits a large skewness or kurtosis, relative to that of either a normal distribution or an exponential distribution. In common use, the terms fat-tailed and heavy-tailed are sometimes synonymous, but sometimes the term fat-tailed is instead defined as a proper subset of heavy-tailed. Different research communities favor one or the other largely for historical reasons, and may have differences in the precise definition of either.

Fat-tailed distributions have been empirically encountered in a variety of areas: physics, earth sciences, economics, and political science. 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. However, fat-tailed distributions also include other slowly-decaying distributions, such as the log-normal.

The opposing counterpart of a fat-tailed distribution is a thin-tailed distribution, whose description has similar ambiguity.