Estimating galaxy luminosity functions.

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.