A case against the lognormal distribution

Abstract

The lognormal distribution is, in some respects, of great simplicity. This is one reason why, next to the Gaussian, it is widely viewed as the practical statistician’s best friend. From the viewpoint described in Chapter E5, it is short-run concentrated and long-run even. This makes it the prototype of the state of slow randomness, the difficult middle ground between the wild and mild state of randomness. Metaphorically, every lognormal resembles a liquid, and a very skew lognormal resembles a glass, which physicists view as a very viscous liquid.

A hard look at the lognormal reveals a new phenomenon of delocalized moments. This feature implies several drawbacks, each of which suffices to make the lognormal dangerous to use in scientific research. Population moments depend overly on exact lognormality. Small sample sequential moments oscillate to excess as the sample size increases. A non-negligible concentration rate can only represent a transient that vanishes for large samples.