Recent observations of the globular clusters in the Milky Way and M31 confirm that their luminosities follow a relatively simple distribution, the globular cluster luminosity function (GCLF), that is unimodal and nearly symmetric. Maximum-likelihood methods are used to fit three simple types of analytic functions to the GCLFs in these two galaxies. The analytic function which best describes the GCLFs is found to be the t distribution with a shape parameter of mu about five. The most probable values of the parameters which characterize the Milky Way GCLF are M(V)0 = -7.29 +/- 0.13 for the peak of 'turnover' magnitude, and sigma(t) = 1.1 +/- 0.1 mag for the dispersion parameter. Similarly, the most probable values for the M31 GCLF are V(0) = 17.00 +/- 0.11 and sigma(t) = 0.82 +/- 0.08 for the turnover magnitude and dispersion. For a M31 distance modulus of (m - M)V = 24.51 +/- 0.1, the absolute magnitude of the M31 halo cluster peak is then M(V)0 = -7.51 +/- 0.15. The GCLF for the M31 halo therefore appears to have a slightly higher mean luminosity and smaller sample dispersion than the Milky Way GCLF, though the differences in both parameters are just on the edge of being statistically significant.