Self-similar Process - The Heavy-tail Distribution

The Heavy-tail Distribution

A distribution is said to have a heavy tail if

$\lim_{x \to \infty} e^{\lambda x}\Pr = \infty \quad \mbox{for all } \lambda>0.\,$

One simple example of a heavy-tailed distribution is the Pareto distribution.

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“There is the illusion of time, which is very deep; who has disposed of it? Mor come to the conviction that what seems the succession of thought is only the distribution of wholes into causal series.”
—Ralph Waldo Emerson (1803–1882)