  We use several quasar samples to determine the density and luminosity
evolution of quasars. Combining different samples and accounting for varying
selection criteria require tests of correlation and the determination of
distributions for multiply truncated data. We describe new non-parametric
techniques for accomplishing these tasks, which have been developed recently by
Efron and Petrosian (1998). We use matter dominated cosmological models with
either zero cosmological constant or zero spatial curvature. Of the two most
common models of luminosity evolution, L = exp(k t(z)) and L = (1+z)^k', we
find the second model to be a better description of the data at all
luminosities; we find k' = 2.58 ([2.14,2.91] one sigma region) for the Einstein
- de Sitter model.
  Using this form of luminosity evolution we determine a global luminosity
function and the evolution of the co-moving density for the two types of
cosmological models. For the Einstein - de Sitter cosmological model we find a
relatively strong increase in co-moving density up to a redshift of about 2, at
which point the density peaks and begins to decrease rapidly. This is in
agreement with results from high redshift surveys. We find some co-moving
density evolution for all cosmological models, with the rate of evolution lower
for models with lower matter density. We find that the local cumulative
luminosity function exhibits the usual double power law behavior. The
luminosity density (i.e. the total rate of energy output of quasars) is found
to increase rapidly at low redshift and to peak at around z = 2. Our results
for the luminosity density are compared to results from high redshift surveys
and to the variation of the star formation rate with redshift.
