  Only the 1/V_max method has been employed so far for observationally
determining the white dwarf luminosity function, whereas for other kind of
luminosity functions several other methods have been frequently used. Moreover,
the procedures to determine the white dwarf luminosity function are not free of
biases. These biases have two different origins: they can either be of
statistical nature or a consequence of the measurement errors. In a previous
paper we carried out an in-depth study of the first category of biases for
several luminosity function estimators. In this paper we focus on the biases
introduced by the measurement errors and on the effects of the degree of
contamination of the input sample used to build the disc white dwarf luminosity
function by different kinematical populations. To assess the extent of these
biases we use a Monte Carlo simulator to generate a controlled synthetic
population and analyse the behaviour of the disc white dwarf luminosity
function for several assumptions about the magnitude of the measurement errors
and for several degrees of contamination, comparing the performances of the
most robust luminosity function estimators under such conditions.
