  This paper uses data obtained from the galaxy luminosity function (LF) to
calculate two types of radial number densities statistics of the galaxy
distribution as discussed in Ribeiro (2005), namely the differential density
$\gamma$ and the integral differential density $\gamma^\ast$. By applying the
theory advanced by Ribeiro and Stoeger (2003), which connects the relativistic
cosmology number counts with the astronomically derived LF, the differential
number counts $dN/dz$ are extracted from the LF and used to calculate both
$\gamma$ and $\gamma^\ast$ with various cosmological distance definitions,
namely the area distance, luminosity distance, galaxy area distance and
redshift distance. LF data are taken from the CNOC2 galaxy redshift survey and
$\gamma$ and $\gamma^\ast$ are calculated for two cosmological models:
Einstein-de Sitter and an $\Omega_{m_0}=0.3$, $\Omega_{\Lambda_0}=0.7$ standard
cosmology. The results confirm the strong dependency of both statistics on the
distance definition, as predicted in Ribeiro (2005), as well as showing that
plots of $\gamma$ and $\gamma^\ast$ against the luminosity and redshift
distances indicate that the CNOC2 galaxy distribution follows a power law
pattern for redshifts higher than 0.1. These findings bring support to
Ribeiro's (2005) theoretical proposition that using different cosmological
distance measures in statistical analyses of galaxy surveys can lead to
significant ambiguity in drawing conclusions about the behavior of the observed
large scale distribution of galaxies.
