Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742.
Proc Natl Acad Sci U S A. 1982 May;79(10):3380-3. doi: 10.1073/pnas.79.10.3380.
It is shown, following Shockley [Shockley, W. (1957) Proc. IRE 45, 279-290], that, when a population is engaged in tasks whose completion requires the successful conclusion of many independent subtasks, the distribution function for successes in the primary task is log normal. It is also shown that, when the dispersion of the log-normal distribution is large, the distribution is mimicked by a 1/x distribution over a wide range of x. This argument provides a generic set of processes that yields the much observed 1/x distribution, and will also lead to a 1/f noise spectrum. It is commonly found that distributions that seem to be log normal over a broad range (say to the 95th percentile of a population) change to an inverse fractional power (Pareto) distribution for the last few percentile. Annual income distributions are examples with this structure. The very wealthy generally achieve their superwealth through amplification processes that are not available to most. We have introduced a simple amplification model to characterize the transition from a log-normal distribution to an inverse-power Pareto tail.
根据 Shockley（Shockley，W.（1957）Proc. IRE 45, 279-290）的研究，当一个群体从事需要成功完成许多独立子任务的任务时，主要任务中成功的分布函数为对数正态分布。还表明，当对数正态分布的离散度较大时，分布在 x 的宽范围内被 1/x 分布模拟。该论点提供了一组通用的过程，产生了广泛观察到的 1/x 分布，并且还将导致 1/f 噪声谱。通常发现，在广泛范围内（例如，在人口的第 95 个百分位数内）似乎呈对数正态分布的分布对于最后几个百分位数会变为倒数分数幂（Pareto）分布。年收入分布就是具有这种结构的示例。非常富有的人通常通过大多数人无法获得的放大过程来实现超级财富。我们引入了一个简单的放大模型来描述从对数正态分布到逆幂 Pareto 尾部的转变。
