Note, that in the limit of large perturbations \sigma(M)\gg \delta_M~, we expect all matter to be contained in halos such that f(\delta_M>\delta_c)=1~. However, the above equation gives us the limit f(\delta_M>\delta_c) = \frac{1}{2}~. One can make an ad-hoc argument and say that negative perturbations are not contributing in this scheme so that we are mistakenly leaving out half of the mass. And so, the Press-Schechter ansatz is
