Getting more out of V/Vm than just the mean
  Banhatti (2009) set down the procedure to derive cosmological number density n(z) from the differential distribution p(x) of the fractional luminosity volume relative to the maximum volume, x \equiv V/Vm (0 \leq x \leq 1), using a small sample of 76 quasars for illustrative purposes. This procedure is here applied to a bigger sample of 286 quasars selected from Parkes half-Jansky flat-spectrum survey at 2.7 GHz (Drinkwater et al 1997). The values of n(z) are obtained for 8 values of redshift z from 0 to 3.5. The function n(z) can be interpreted in terms of redshift distribution obtained by integrating the radio luminosity function {\rho}(P, z) over luminosities P for the survey limiting flux density S0 = 0.5 Jy. Keywords. V/Vm - luminosity-volume - cosmological number density - redshift distribution - luminosity function - quasars [Note: This somewhat modified version was submitted to MNRaS on 14 July 2016. It was (almost) rejected, except if thoroughly revised.] 
Dilip G Banhatti (School of Physics, Madurai Kamaraj University,   India)
astro-ph.CO astro-ph.IM