TS distribution (left side) and p-distribution (right side) of a simulated empty field, with g_gal = 0 and g_iso = 5, flux free, and position and spectral parameters fixed. The blue crosses indicate the calculated distribution, the black line indicates the best fit, the red dotted line indicates the theoretical distribution, the green dashed line indicates the χ₁ theoretical distribution, and the cyan dash-dotted line indicates the distribution.