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The small scatter in the luminosities of the brightest galaxies in clusters has been a topic of much debate. It has been argued that these galaxies are either special objects or the tail-end of a statistical distribution. In 1928, Fisher and Tippett derived the general form a distribution of extreme sample values should take, independent of the parent distribution from which they are drawn. We compare this asymptotic form with the distribution of first ranked cluster members and conclud that these galaxies are not the extreme members of a statistical population. On the other hand, comparison of first ranked members of ‘loose’ groups with the extreme value distributions shows that these galaxies are consistent with their being the tail-end of a statistical distribution.
Bhavsar et al. (Mon,) studied this question.