Hubble Space Telescope 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 cluster populations. The basis of our approach is the construction of synthetic cluster color-magnitude-radius diagrams (CMRDs), which we compare with the observed data using a maximum likelihood calculation. This approach permits a relatively easy incorporation of incompleteness ( a function of not only magnitude and color, but also radius), photometry errors and biases, and a variety of other complex effects into the calculation, instead of the more common procedure of attempting to correct for those effects. We then apply this procedure to our NGC 3627 data from Paper I. We find that we are able to successfully model the observed CMRD and constrain a number of parameters of the cluster population. We measure a power-law mass function slope of alpha = 1.50 +/- 0.07 and a distribution of core radii centered at r(c) = 1.53 +/- 0.15 pc. Although the extinction distribution is less constrained, we measured a value for the mean extinction consistent with that determined in Paper I from the Cepheids.