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A method for estimating the void probability function (VPF) from any volume- and absolute magnitude-limited galaxy catalog is developed and applied to three volume- and magnitude-limited subclasses from the CfA catalog which involve different luminosity classes. The VPF is calculated for each subclass and the count probability of finding N galaxies in a volume V is calculated for N = 1 to 4, successively. It is shown that each of the samples obeys a scaling invariance predicted by the class of hierarchical models, suggesting that this property applies to the whole galaxy distribution. This result permits a comparison of the VPFs for the three samples, and is it shown that bright galaxies are more clustered than faint ones in the samples studied. Estimations of the two-point correlation functions show that bright and faint galaxies appear to obey a universal distribution.
Maurogordato et al. (Tue,) studied this question.