The case against intermediate statistics

Abstract

It is shown that intermediate statistics do not correspond to any physical process. The stationary probability distributions of intermediate statistics are not compatible with any mechanism which allows a variation between Fermi–Dirac and Bose–Einstein statistics. The binomial and negative binomial distributions, characterizing Fermi–Dirac and Bose–Einstein statistics, respectively, transform into the Poisson distribution, descriptive of classical statistics, as the number of energy cells increases without limit. These distributions are shown to be the laws of error leading to the average value as the most probable value.