On the simultaneous analysis of several complete samples. The V/Vmax and Ve/Va variables, with applications to quasars.

Methods are derived for applying the V/Vmax variable when several complete samples are analyzed simultaneously. A new, related, variable, V(e)/V(a), which is superior to V/Vmax when sufficient observational data are available, is introduced. It is shown how statistically independent complete samples can be generated from partially overlapping samples such that each observed object appears only once in the analysis. These methods make it possible to combine the information from different complete samples, and to make an efficient use of all available data. Illustrative examples for quasars are given. It is shown how the generalized V/Vmax and V(e)/V(a) can be used to find the amount of cosmological evolution of quasars and its associated range of uncertainty.