Bias (top) and standard deviation (bottom) averaged over bins of the estimated fractional parallax uncertainty f_app for four estimators of the distance: the maximum likelihood (ML) estimator (orange), the ML estimator corrected as described in Smith & Eichhorn (1996) (light blue), the mode of the posterior obtained with an exponentially decreasing space density (EDSD) prior and L = 1.35 kpc (dark green), and the mode of the posterior obtained with a uniform distance (UD) prior truncated at 100 kpc (red).