  We revisit the properties and astrophysical implications of the field white
dwarf mass distribution in preparation of Gaia applications. Our study is based
on the two samples with the best established completeness and most precise
atmospheric parameters, the volume-complete survey within 20 pc and the Sloan
Digital Sky Survey (SDSS) magnitude-limited sample. We explore the modelling of
the observed mass distributions with Monte Carlo simulations, but find that it
is difficult to constrain independently the initial mass function (IMF), the
initial-to-final-mass relation (IFMR), the stellar formation history (SFH), the
variation of the Galactic disk vertical scale height as a function of stellar
age, and binary evolution. Each of these input ingredients has a moderate
effect on the predicted mass distributions, and we must also take into account
biases owing to unidentified faint objects (20 pc sample), as well as unknown
masses for magnetic white dwarfs and spectroscopic calibration issues (SDSS
sample). Nevertheless, we find that fixed standard assumptions for the above
parameters result in predicted mean masses that are in good qualitative
agreement with the observed values. It suggests that derived masses for both
studied samples are consistent with our current knowledge of stellar and
Galactic evolution. Our simulations overpredict by 40-50% the number of massive
white dwarfs (M > 0.75 Msun) for both surveys, although we can not exclude a
Salpeter IMF when we account for all biases. Furthermore, we find no evidence
of a population of double white dwarf mergers in the observed mass
distributions.
