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→Relationship to fat-tailed distributions
A [[fat-tailed distribution]] is a distribution for which the probability density function, for large x, goes to zero as a power <math>x^{-a}</math>. 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]] {{Contradict-inline|article=fat-tailed distribution|reason=Fat-tailed page says log-normals are in fact fat-tailed.|date=June 2019}}. Many other heavy-tailed distributions such as the [[log-logistic distribution|log-logistic]] and [[Pareto distribution|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 <math>x^{-a}</math>. 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]] {{Contradict-inline|article=fat-tailed distribution|reason=Fat-tailed page says log-normals are in fact fat-tailed.|date=June 2019}}. Many other heavy-tailed distributions such as the [[log-logistic distribution|log-logistic]] and [[Pareto distribution|Pareto]] distribution are, however, also fat-tailed.
胖尾分布是这样的分布：对于大x，概率密度函数作为幂<math>x^{-a}</math>变为零。由于幂总是受到指数分布的概率密度函数的限制，因此，胖尾分布始终是重尾分布。但是，某些分布的尾部趋近于零的速率比指数函数慢（表示它们是重尾），而比幂快（表示它们不是胖尾）。例如对数正态分布。当然，许多其他的重尾分布，例如对数逻辑分布和帕累托分布也属于胖尾分布。
== Estimating the tail-index{{definition|date=January 2018}} ==
== Estimating the tail-index{{definition|date=January 2018}} ==