A distribution in which the probability of an extreme value is greater than it would be for a normal distribution having the same quartiles. For the random variable X, one definition is that the distribution has a heavy right tail if![heavy-tailed distribution](Images/oree/doc/10.1093/acref/9780199679188.001.0001/acref-9780199679188-math-0271-full.gif)
If, in addition the distribution satisfies the requirement that, for all t > 0, ![heavy-tailed distribution](Images/oree/doc/10.1093/acref/9780199679188.001.0001/acref-9780199679188-math-0272-full.gif)
then the distribution is said to have a long right tail and may be described as a long-tailed distribution.
Examples of heavy-tailed distributions are the Cauchy distribution, the lognormal distribution, the Pareto distribution, and the t-distribution.