[求助]power law tails是什么意思。

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全句是这样的：Many real problems in finance and hydrology involve data sets with power law tails.请教该如何翻译。

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关键词：Power 是什么意思 tails tail law 意思 law Power tails

没有人懂吗？还是高手不愿意回答。

power law 应当是幂指数律的意思，power law tails是服从幂指数律分布的尾部，好像是比正态分布的尾部厚一些，跟幂次有关系。请高手做进一步说明。

一般的随机游走应该都是正态分布假定，但资本市场中，常出现翘尾现象（fat tails），分形理论应该是专门研究这个的，

这句话的意思是：许多现实的金融和水文学问题包括有服从幂次律的数据序列。

更加不懂了

在一般的金融理论里，证券价格被假定服从正态分布，著名的布-斯期权定价公式就以正态分布为基础。但实证研究发现证券价格并不服从正态分布，而是服从一种尖峰厚尾的分布，就是说，出现极端数据的概率比正态分布的概率要大，用幂次分布拟合的效果比正态分布拟合的效果好，而水文学中洪峰事件可能也是服从类似的分布。

哪幂次分布的分布函数是什么。

the following word is what I found from a essay,

previous work(Xavier et al, Nature423 2003 ) analyzed the distribution of R for the 1000 largest US stocks and several major international indexes and found a power-law distrubution P{[R]>x} ~x(-n), where n~=3, which si called the cuboc law of returns.

Power Law Tails is developed from Zipf's Law.

In an investing context, we might expect to encounter this law in some
important instances: (a) the capitalization of stocks in the S&P 500 index and
(b) the capitalization of a large number of similar traders in a market, and
perhaps (c) the distribution of sizes of trading firms. Empirical evidence has
been published supporting (a) and (b).

A related law governs distribution of log returns of securities without the
requirement of a slope of -1. For a given security, this law will take the form
P[R>r]~ 1/(r^k), for large r
where R is a random variable of asset or portfolio returns and is a constant.
Note that the probability density function (if it exists) will have a tail
~ 1/[r^(k+1)]. A probability distribution that has this property is said to have power law tails.

In distributions with power law tails, the
occurrence of large deviations is much more likely than in those with
exponentially decaying tails.

A Theory of Power Law Distributions in Financial Fluctuations,
by Xavier Gabaix, et. al., contained in his home page
http://pages.stern.nyu.edu/~xgabaix/.