A critical analysis of high-redshift, massive galaxy clusters: I
  We critically investigate current statistical tests applied to high redshift
clusters of galaxies in order to test the standard cosmological model and
describe their range of validity. We carefully compare a sample of
high-redshift, massive, galaxy clusters with realistic Poisson sample
simulations of the theoretical mass function, which include the effect of
Eddington bias. We compare the observations and simulations using the following
statistical tests: the distributions of ensemble and individual existence
probabilities (in the >M,>z sense), the redshift distributions, and the 2d
Kolmogorov-Smirnov test. Using seemingly rare clusters from Hoyle et al.
(2011), and Jee et al. (2011) and assuming the same survey geometry as in Jee
et al. (2011, which is less conservative than Hoyle et al. 2011), we find that
the (>M,>z) existence probabilities of all clusters are fully consistent with
LCDM. However assuming the same survey geometry, we use the 2d K-S test
probability to show that the observed clusters are not consistent with being
the least probable clusters from simulations at >95% confidence, and are also
not consistent with being a random selection of clusters, which may be caused
by the non-trivial selection function and survey geometry. Tension can be
removed if we examine only a X-ray selected sub sample, with simulations
performed assuming a modified survey geometry.
