A Method of Allowing for Known Observational Selection in Small Samples Applied to 3CR Quasars

A useful method is developed which minimizes numerical fluctuations when deriving luminosity functions and density evolution from data subject to observational selection. The distribution of ratios of radio power to optical power for quasars is derived from the 3CR quasars; this is a steeply rising function in agreement with the observation that most quasars are radio quiet. The density evolution of the quasi-stellar sources is derived direct from the data and a possible interpretation is an exponential decay with cosmic time. The density evolution is then used to determine the optical luminosity function of quasars. There appears to be a sharp upper limit to the optical luminosity; however, at the faint end the luminosity function is still increasing exponentially, so that most quasar light comes from the dimmest quasars.