A Theoretical Model for Mars Crater-Size Frequency Distribution
  We present a theoretical and analytical curve with reproduce essential features of the frequency distributions vs. diameter, of the 42,000 crater contained in the Barlow Mars Catalog. The model is derived using reasonable simple assumptions that allow us to relate the present craters population with the craters population at each particular epoch. The model takes into consideration the reduction of the number of craters as a function of time caused by their erosion and obliteration, and this provides a simple and natural explanation for the presence of different slopes in the empirical log-log plot of number of craters (N) vs. diameter (D). 
W.A. Bruckman, A. Ruiz, E. Ramos (University of Puerto Rico at   Humacao)