Statistical Models for Globular Cluster Luminosity Distribution

We consider statistical models which have been proposed for luminosity distributions for the globular clusters in the Milky Way and M31. Although earlier research showed that the cluster luminosity functions in those two galaxies were well fit by Gaussian distributions, subsequent investigations suggested that their luminosities were better fit by t-, rather than Gaussian, distributions. By applying the Bayesian Information Criterion, we do not find overwhelming statistical evidence that the t-distribution is superior to the Gaussian distribution as a model of luminosity distribution for the Milky Way. In the case of M31, we find moderate evidence that the Gaussian distribution is superior to the t-distribution. In neither case do we find strong evidence to support the use of one distribution over the other as a statistical model for the luminosities of the globular clusters in the Milky Way and M31. Consequently, we recommend that the Gaussian be retained as the statistical model for luminosity distribution. Moreover, we urge caution in the use of the KolmogorovSmirnov statistic to justify the choice of statistical models for globular cluster luminosity functions.