of cluster galaxies, the most luminous of them form a hump at the bright end (e.g., @colless [@yagi; @2pigg]). Yet, at the same time, there is little variation in magnitude among them [@hs; @pl; @bernardi; @linden]. This ties in with the fact that the luminosity of BCGs is expected to vary only slowly with increasing cluster luminosity (@lm; see also the results for the mass luminosity relation of central galaxies in @paper2).

In order to try to answer this problem from available observational data, two different indicators have been considered. One is the shape of the overall distribution of the magnitude of BCGs. If BCGs are merely the extreme cases of a general distribution applicable to all cluster galaxies, then it is expected that results from extreme value theory in statistics apply, predicting a resulting distribution shaped like the Gumbel distribution [@bb84; @bb]. On the other hand, if BCGs are considered a special, distinct type of galaxy, then some particular distribution is to be expected, such as a Gaussian [@pl] or lognormal. Some studies have also raised the possibility that it could be actually a combination of the two, probably depending on the type of cluster [@bhavsar; @bb].

The other 