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A new class of tests of a statistical model of the luminosities of cluster galaxies is derived and applied to data obtained by Sandage and Hardy. The tests are novel in that they are independent of both the assumed luminosity function and its variation from cluster to cluster. The tests also appear to be insensitive to possible selection effects. The results are not conclusive, but they suggest that the luminosity of the brightest cluster galaxy is determined by some physical process, rather than by a statistical sampling of a luminosity function. Subject headings: galaxies: clusters of - galaxies: photometry
Tremaine et al. (Tue,) studied this question.