  In this work a comparison between different galaxy luminosity function
estimators by means of Monte-Carlo simulations is presented. The simulations
show that the C- method of Lynden-Bell (1971) and the STY method derived by
Sandage, Tammann & Yahil (1979) are the best estimators to measure the shape of
the luminosity function. The simulations also show that the STY estimator has a
bias such that the faint-end slope is underestimated for steeper inclinations
of the Schechter Function, and that this bias becomes quite severe when the
sample contains only a few hundred objects. Overall, the C- is the most robust
estimator, being less affected by different values of the faint end slope of
the Schechter parameterization and sample size. The simulations are also used
to compare different estimators of the luminosity function normalization. They
demonstrate that most methods bias the recovered mean density towards values
which are about 20% lower than the input value.
