[ITAL]Hubble Space Telescope[/ITAL] Survey of Clusters in Nearby Galaxies. II. Statistical Analysis of Cluster Populations

We present a statistical system that can be used in the study of clusterpopulations. The basis of our approach is the construction of synthetic clustercolor-magnitude-radius diagrams (CMRDs), which we compare with the observeddata using a maximum likelihood calculation. This approach permits a relativelyeasy incorporation of incompleteness (a function of not only magnitude andcolor, but also radius), photometry errors and biases, and a variety of othercomplex effects into the calculation, instead of the more common procedure ofattempting to correct for those effects. We then apply this procedure to our NGC 3627 data from Paper I. We find thatwe are able to successfully model the observed CMRD and constrain a number ofparameters of the cluster population. We measure a power law mass functionslope of alpha = -1.50 +/- 0.07, and a distribution of core radii centered atr_c = 1.53 +/- 0.15 pc. Although the extinction distribution is lessconstrained, we measured a value for the mean extinction consistent with thatdetermined in Paper I from the Cepheids.Comment: 21 pages, 3 figures accepted for publication by A