Simulation results for the Gaussian (left panel) and log-normal (right panel) fit in the two different magnitude bins. In the leftmost column, we show maximum likelihood contours at 68%, 95%, and 99% c.l. in green, blue, and red, respectively; the red cross indicates the position of the best fit parameters. The rightmost column shows the histogram of the observed data and the relevant best-fit distribution. The red continuous line is the intrinsic PDF(β), which is transformed into the blue continuous line by observational effects.