Germanium nanocrystals (NCs) were formed by in-situ thermal annealing of an amorphous Ge layer deposited by molecular beam epitaxy on a thin SiO2 layer on Si(001). The Ge NCs were then capped in situ with a thin layer of amorphous Si to prevent oxidation. For the present range of particle sizes (2.5 to 60 nm), the NC photoluminescence (PL) appeared primarily as a wide near-infrared band peaked near 800 meV. The peak energy of the PL band reflects the average NC size and its shape depends on the NC size distribution. Using both the k·p and tight binding theoretical models, we have analyzed the PL spectrum in terms of the NC size distribution required to reproduce the observed asymmetric band shape, which includes, for the smaller diameter NCs, a band gap enlargement due to quantum confinement. The observed size distribution determined from transmission electron microscopy analysis allowed the determination of the nonlinear increase in the PL quantum efficiency with decreasing NC diameter. This implies that, given a good theoretical description of the system, it is possible to evaluate the size distribution of semiconductor NCs from their PL energy dependence.