  Over the years, several methods have been proposed to compute galaxy
luminosity functions, from the most simple ones -counting sample objects inside
a given volume- to very sophisticated ones -like the C- method, the STY method
or the Choloniewski method, among others. However, only the V/Vmax method is
usually employed in computing the white dwarf luminosity function and other
methods have not been applied so far to the observational sample of
spectroscopically identified white dwarfs. Moreover, the statistical
significance of the white dwarf luminosity function has also received little
attention and a thorough study still remains to be done. In this paper we
study, using a controlled synthetic sample of white dwarfs generated using a
Monte Carlo simulator, which is the statistical significance of the white dwarf
luminosity function and which are the expected biases. We also present a
comparison between different estimators for computing the white dwarf
luminosity function. We find that for sample sizes large enough the V/Vmax
method provides a reliable characterization of the white dwarf luminosity
function, provided that the input sample is selected carefully. Particularly,
the V/Vmax method recovers well the position of the cut-off of the white dwarf
luminosity function. However, this method turns out to be less robust than the
Choloniewski method when the possible incompletenesses of the sample are taken
into account. We also find that the Choloniewski method performs better than
the V/Vmax method in estimating the overall density of white dwarfs, but misses
the exact location of the cut-off of the white dwarf luminosity function.
