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
If, in addition the distribution satisfies the requirement that, for all t > 0, 
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.