Determining proportions of lunar crater populations by fitting crater size distribution

We determine the proportions of two mixed crater populations distinguishable by size distributions on the Moon. A "multiple power-law" model is built to formulate crater size distribution $N(D) \propto D^{-\alpha}$ whose slope $\alpha$ varies with crater diameter $D$. Fitted size distribution of lunar highland craters characterized by $\alpha = 1.17 \pm 0.04$, $1.88 \pm 0.07$, $3.17 \pm 0.10$ and $1.40 \pm 0.15$ for consecutive $D$ intervals divided by 49, 120 and 251 km and that of lunar Class 1 craters with a single slope $\alpha = 1.96 \pm 0.14$, are taken as Population 1 and 2 crater size distribution respectively, whose sum is then fitted to the size distribution of global lunar craters with $D$ between 10 and 100 km. Estimated crater densities of Population 1 and 2 are $44 \times 10^{-5}$ and $5 \times 10^{-5}$ km$^{-2}$ respectively, leading to the proportion of the latter $10 \%$. The results underlines the need for considering the Population 1 craters and the relevant impactors, the primordial main-belt asteroids which dominated the late heavy bombardment.