)The distribution of a random variable "X" with distribution function "F" is said to have a heavy (right) tail if the moment generating function of "X", "MX"("t"), is infinite for all "t" > 0.That means

An implication of this is that

This is also written in terms of the tail distribution function

as

The distribution of a random variable "X" with distribution function "F" is said to have a long right tail if for all "t" > 0,

or equivalently

This has the intuitive interpretation for a right-tailed long-tailed distributed quantity that if the long-tailed quantity exceeds some high level, the probability approaches 1 that it will exceed any other higher level.