T_s distribution (left side) and p-distribution (right side) of a simulated empty field, with g_gal = 1 and g_iso = 6 (where these parameters are allowed to vary during the analysis), flux free, and position fixed. The bluecrosses are the calculated distribution, the black line is the best fit according to Eq. (3), the red dotted line is the theoretical distribution, the green dashed line is the theoretical distribution, and the cyan dotted-dashed line is the distribution.