Some statistical remarks on the Giant GRB Ring
  We studied some statistical properties of the spatial point process displayed
by GRBs of known redshift. To find ring like point patterns we developed an
algorithm and defined parameters to characterize the level of compactness and
regularity of the rings found in this procedure. Applying this algorithm to the
GRB sample we identified three more ring like point patterns. Although, they
had the same regularity but much less level of compactness than the original
GRB ring. Assuming a stochastic independence of the angular and radial
positions of the GRBs we obtained 1502 additional samples, altogether 542222
data points, by bootstrapping the original one. None of these data points
participated in rings having similar level of compactness and regularity as the
original one. Using an appropriate kernel we estimated the joint probability
density of the angular and radial variables of the GRBs. Performing MCMC
simulations we obtained 1502 new samples, altogether 542222 data points. Among
these data points only three represented ring like patterns having similar
parameters as the original one. By defining a new statistical variable we
tested the independence of the angular and radial variables of the GRBs. We
concluded that despite the existence of local irregularities in the GRBs'
spatial distribution (e.g. the GGR) one can not reject the Cosmological
Principle, based on their spatial distribution as a whole. We pointed out the
large scale spatial pattern of the GRB activity does not necessarily re ects
the large scale distribution of the cosmic matter.
