Ensembles of particles obeying Fermi-Dirac statistics are considered from a point of view which is analogous to some recent work of Mayer on classical particle statistics. The density functions ρn are defined for n much smaller than the average number of particles in the ensemble. Since the knowledge of only a few ρn is sufficient for the computation of most averages of physical interest, it is important to compare different ensembles with the same density functions, say ρ1 and ρ2. The ensemble with the largest entropy is constructed as being the most significant. A number of simple examples are briefly considered.