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In probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution. In many applications it is the right tail of the distribution that is of interest, but a distribution may have a heavy left tail, or both tails may be heavy.
In probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution. In many applications it is the right tail of the distribution that is of interest, but a distribution may have a heavy left tail, or both tails may be heavy.
在概率论中，重尾分布是指其尾部呈现出不受指数限制的概率分布：也就是说，它们的尾部比指数分布“重”。在许多应用中，关注的是分布的右尾，但是分布的左尾可能也很重，或者两个尾都很重。
There are three important subclasses of heavy-tailed distributions: the fat-tailed distributions, the long-tailed distributions and the subexponential distributions. In practice, all commonly used heavy-tailed distributions belong to the subexponential class.
There are three important subclasses of heavy-tailed distributions: the fat-tailed distributions, the long-tailed distributions and the subexponential distributions. In practice, all commonly used heavy-tailed distributions belong to the subexponential class.
重尾分布有三个重要的子类：肥尾分布，长尾分布和次指数分布。实际上，所有常用的重尾分布都属于次指数类分布。
There is still some discrepancy over the use of the term heavy-tailed. There are two other definitions in use. Some authors use the term to refer to those distributions which do not have all their power moments finite; and some others to those distributions that do not have a finite variance. The definition given in this article is the most general in use, and includes all distributions encompassed by the alternative definitions, as well as those distributions such as log-normal that possess all their power moments, yet which are generally considered to be heavy-tailed. (Occasionally, heavy-tailed is used for any distribution that has heavier tails than the normal distribution.)
There is still some discrepancy over the use of the term heavy-tailed. There are two other definitions in use. Some authors use the term to refer to those distributions which do not have all their power moments finite; and some others to those distributions that do not have a finite variance. The definition given in this article is the most general in use, and includes all distributions encompassed by the alternative definitions, as well as those distributions such as log-normal that possess all their power moments, yet which are generally considered to be heavy-tailed. (Occasionally, heavy-tailed is used for any distribution that has heavier tails than the normal distribution.)
在使用“重尾”一词时仍存在一些歧义。于是就出现了另外两种定义。一些作者使用该术语来指代那些并非所有幂矩都是有限的分布。也有其它一些人以此指代没有有限方差的分布。本文中给出的是最常用的定义，包括替代定义所涵盖的所有分布，以及具有所有幂矩的对数正态分布，但通常被认为是重尾的。（有时“重尾”用于任何具有比正态分布更重尾巴的分布。）