more complicated one based on the distribution of concentrations at a given halo mass, which fully motivates the introduction of scatter in the CLF without any free parameters. For the satellite galaxies we will use the same modified mass-luminosity relation as well, since these were central galaxies within their own independent haloes prior to merging, so it is reasonable to expect the same effects to apply to them. From semi-analytical modelling, it has been shown that this is a good approximation, although a more careful treatment shows a slightly different relation for sattelites than for central galaxies [@wang]. But note that, when doing analytical calculations, using the subhalo mass function already introduces a form of distribution for the subhaloes as well (in that the mass of a given subhalo can be drawn from it, see section 5.1 for further discussion).

Lognormal model
---------------

The simplest CLF model we consider is to assume it has a lognormal form. This is similar to what was done previously by other authors [@cooray; @coorayc], and such a form seems a good match to the distribution of stellar mass obtained in semi-analytic modelling [@wang]. The problem with this approach is that there is no [*a 