Power Law Tails in Log Normal Data

Empirical distributions of magnitudes such as income, wealth, and firm size are often characterized as lognormal with power law upper tails. This Demonstration illustrates how the upper tail of lognormally distributed data can appear to conform to a power law. A thousand random points from a lognormal distribution are generated and the log of the size is regressed on the log of the rank. If only the top percentiles of points are included in the regression, R-squareds of over 0.98 are not uncommon.