Example luminosity functions ϕ(L) = dP/dln(L) induced by a Gaussian apparent structure model (Eqs. (10), left-hand panel) and a power law apparent structure model (Eqs. (13)) with a luminosity profile slope α = 3 (right-hand panel), both with a core half-opening angle θ_c = 0.1 rad and = 10⁵³ erg s⁻¹. In each panel, the luminosity function corresponding to a population with zero core dispersion (A → ∞ in Eq. (2)) is shown in grey, and three cases with different core luminosity distributions (slopes reported in the legend) are shown with coloured lines. The corresponding L_c distributions (arbitrarily scaled) are shown with dashed lines. In the right-hand panel, the dashed black line shows the trend ϕ(L)∝L^−2/α_L expected at intermediate luminosities.