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→Definitions
==Definitions==
== Definitions 定义 ==
===Definition of heavy-tailed distribution===
=== Definition of heavy-tailed distribution 重尾分布的定义 ===
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===Definition of long-tailed distribution===
=== Definition of long-tailed distribution 长尾分布的定义 ===
The probabilistic interpretation or catastrophe principle.
The probabilistic interpretation or catastrophe principle.
===Subexponential distributions===
=== Subexponential distributions 长尾分布的定义 ===
A fat-tailed distribution is a distribution for which the probability density function, for large x, goes to zero as a power x^{-a}. Since such a power is always bounded below by the probability density function of an exponential distribution, fat-tailed distributions are always heavy-tailed. Some distributions, however, have a tail which goes to zero slower than an exponential function (meaning they are heavy-tailed), but faster than a power (meaning they are not fat-tailed). An example is the log-normal distribution . Many other heavy-tailed distributions such as the log-logistic and Pareto distribution are, however, also fat-tailed.
A fat-tailed distribution is a distribution for which the probability density function, for large x, goes to zero as a power x^{-a}. Since such a power is always bounded below by the probability density function of an exponential distribution, fat-tailed distributions are always heavy-tailed. Some distributions, however, have a tail which goes to zero slower than an exponential function (meaning they are heavy-tailed), but faster than a power (meaning they are not fat-tailed). An example is the log-normal distribution . Many other heavy-tailed distributions such as the log-logistic and Pareto distribution are, however, also fat-tailed.
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.
==Common heavy-tailed distributions==
==Common heavy-tailed distributions==