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Fat-tailed distribution : ウィキペディア英語版
Fat-tailed distribution

A fat-tailed distribution is a probability distribution that has the property, along with the other heavy-tailed distributions, that it exhibits large skewness or kurtosis. This comparison is often made relative to the normal distribution, or to the exponential distribution. Fat-tailed distributions have been empirically encountered in a variety of areas: economics, physics, and earth sciences. Some fat-tailed distributions have power law decay in the tail of the distribution, but do not necessarily follow a power law everywhere.
==Definition==

The distribution of a random variable ''X'' is said to have a fat tail if
:
\Pr() \sim x^\textx \to \infty,\qquad \alpha > 0.\,

That is, if ''X'' has probability density function f_X(x),
:
f_X(x) \sim x^ \textx \to \infty, \qquad \alpha > 0.\,

Here the tilde notation " \sim " refers to the asymptotic equivalence of functions.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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