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→Definition of long-tailed distribution 长尾分布的定义
The distribution of a [[random variable]] ''X'' with [[cumulative distribution function|distribution function]] ''F'' is said to have a long right tail<ref name="Asmussen"/> if for all ''t'' > 0,
The distribution of a [[random variable]] ''X'' with [[cumulative distribution function|distribution function]] ''F'' is said to have a long right tail<ref name="Asmussen"/> if for all ''t'' > 0,
The distribution of a random variable X with distribution function F is said to have a long right tail[1] if for all t > 0,
如果对于所有t>0，具有分布函数F的随机变量X的分布具有较长的右尾，
:<math>
\lim_{x \to \infty} \Pr[X>x+t\mid X>x] =1, \,
<math>
or equivalently
或等同于
:<math>
\overline{F}(x+t) \sim \overline{F}(x) \quad \mbox{as } x \to \infty. \,
</math>
F i ([0，infty))是。这里 i ([0，infty))是正半直线的指示函数。或者，实数行上支持的随机变量 x 是子指数当且仅当 x ^ + = max (0，x)是子指数。
F i ([0，infty))是。这里 i ([0，infty))是正半直线的指示函数。或者，实数行上支持的随机变量 x 是子指数当且仅当 x ^ + = max (0，x)是子指数。
All subexponential distributions are long-tailed, but examples can be constructed of long-tailed distributions that are not subexponential.
All subexponential distributions are long-tailed, but examples can be constructed of long-tailed distributions that are not subexponential.
所有的次指数分布都是长尾分布，但是例子可以由非次指数的长尾分布构造。
所有的次指数分布都是长尾分布，但是例子可以由非次指数的长尾分布构造。
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.
All long-tailed distributions are heavy-tailed, but the converse is false, and it is possible to construct heavy-tailed distributions that are not long-tailed.
</math>
</math>
=== Subexponential distributions 长尾分布的定义 ===
=== Subexponential distributions 长尾分布的定义 ===