Distribution of Maximal Luminosity of Galaxies in the Sloan Digital Sky
  Survey
  Extreme value statistics (EVS) is applied to the distribution of galaxy
luminosities in the Sloan Digital Sky Survey (SDSS). We analyze the DR8 Main
Galaxy Sample (MGS), as well as the Luminous Red Galaxies (LRG). Maximal
luminosities are sampled from batches consisting of elongated pencil beams in
the radial direction of sight. For the MGS, results suggest a small and
positive tail index $\xi$, effectively ruling out the possibility of having a
finite maximum cutoff luminosity, and implying that the luminosity distribution
function may decay as a power law at the high luminosity end. Assuming,
however, $\xi=0$, a non-parametric comparison of the maximal luminosities with
the Fisher-Tippett-Gumbel distribution (limit distribution for variables
distributed by the Schechter fit) indicates a good agreement provided
uncertainties arising both from the finite batch size and from the batch size
distribution are accounted for. For a volume limited sample of LRGs, results
show that they can be described as being the extremes of a luminosity
distribution with an exponentially decaying tail, provided the uncertainties
related to batch-size distribution are taken care of.
