In this report on examples of distribution functions with long tails we (a) show
that the derivation of distributions with inverse power tails from a maximum
entropy formalism would be a consequence only of an unconventional auxilliary
condition that involves the specification of the average value of a complicated
logarithmic function, (b) review several models that yield log-normal distribu-
tions, (c) show that log normal distribulions may mimic 1/f noise over a certain
range, and (d) present an amplification model to show how log-normal personal
income distributions are transformed into inverse power (Pareto) distributions in
the high income range.