Under the proviso that the existing tight-binding (TB) and effective mass (EM) theoretical models provide a good description of the Ge dot energy gap versus dot diameter, this work investigates the effect of nanoparticle size and the size distribution on the near infrared PL spectrum obtained from self-assembled Ge dots grown on a thin layer of TiO_\textrm2 or SiO_\textrm2 on Si. For the as-grown samples, the dot PL emission occupies a wide near-infrared band between 0.8 and 1 eV. The PL efficiency versus dot size for four samples was obtained in three steps. Firstly, the PL spectrum was converted to an intensity plot versus dot diameter rather than energy by taking the PL emission from each dot to occur at the dot bandgap calculated using the TB or EM model. Secondly, a numerical form for the physical size distribution of that sample was obtained by performing a least-squares fit of a Gaussian to the dot size distribution measured by atomic force microscopy or transmission electron microscopy. Finally, the PL efficiency versus dot size was calculated using the fitted Gaussian dot size distribution to normalize the PL intensity distribution obtained in the first step. Although the absolute intensities of the PL from the samples vary, the calculated curves are all well-fitted by straight lines on a log-log plot with essentially the same slope for all samples, which indicates that under weak confinement there is a universal power-law increase in PL efficiency with decreasing dot size.