Power Law Tails is developed from Zipf's Law.

In an investing context, we might expect to encounter this law in someimportant 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, andperhaps (c) the distribution of sizes of trading firms. Empirical evidence hasbeen published supporting (a) and (b).

A related law governs distribution of log returns of securities without therequirement of a slope of -1. For a given security, this law will take the formP[R>r]~ 1/(r^k), for large rwhere 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, theoccurrence of large deviations is much more likely than in those withexponentially decaying tails.

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