The values of r and f are all that is needed to describe the mechanism and are the components of the transition matrix. The transition matrix can be used to find the equilibrium values for the occupancy of the states. These values are unchanged when multiplied by the transition matrix. To get the number of earthquakes in each magnitude interval one multiplies the equilibrium values by r_k. In the plot below logN is the logarithm of the number of earthquakes observed and logN_fit is the logarithm of the number computed from the equilibrium values. Note that this mechanism does have a peak unlike the linear fit found previously. The Poisson distribution does not appear to be an equilibrium distribution. k is the value of k used in the Poisson fit and is approximately 140 + M/ΔM with ΔM = 0.1. The peak is at M 1.1 (k = 151) and there are 10 intervals per M 1.0 step.