Zipf's Law and Prior Distributions for the Composition of a Population

The limiting distribution of frequencies of frequencies as the population size becomes large is obtained under Bose-Einstein and Maxwell-Boltzmann forms of the classical occupancy problem, when the number of cells is random and has a prior distribution. A rich variety of limiting distributions is obtained, including weak forms of Zipf's Law and the Fisher logarithmic series distribution. Lizards are compared to the weak form of Zipf's Law, and some speculations are made in regard to this law.