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A parametric likelihood analysis of the joint redshift-luminosity distribution is presented for a composite, complete sample of 32 quasars with B between 17.0 and 19.2 selected on the basis of ultraviolet excess. Best estimates and joint confidence regions are determined for the parameters of several models of the quasar optical luminosity and evolution function. These models are also tested explicitly for their acceptability. A steeper luminosity function is found than was found for previous samples. A model invoking pure density evolution is rejected on the basis of its extrapolation to fainter magnitudes through comparisons with the optical number counts and independently with the observed 2 keV X-ray background. Assuming an average value for L(x)/L(opt), the contribution of quasars to the X-ray background at 2 keV is discussed.
Marshall et al. (Wed,) studied this question.