A Simplified Fit for the Earthquake Distribution

I wrote a new routine to improve on a fit for the gain function and adopted a form for g that would guarantee a linear slope for the log of the number of earthquakes at the larger magnitudes. The rms error for the fit is 0.105546 which was only a slight improvement on the fit done by eye assuming a polynomial form for the log of g. The new empirical formula for g was suggested by the previous fit. One would also expect a continuation of the linear slope for larger magnitudes from what we know about the number of global earthquakes above M 5.0.