Heavy-Tailed Distributions

The distribution \(\mathbb{P}\) of a random variable \(X\) is said to be heavy-tailed for \(\forall \epsilon>0\) \[ \lim_{x\to \infty} \frac{\mathbb{P}(X>x)}{e^{\epsilon x}} = \infty\]

If \(\exists \epsilon >0\) such that the quantity above is finite, it is called light-tailed.