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We have written a new equation to study the statistics of earthquakedistributions. We call this equation "the generalized logistic equation". TheGutenberg-Richter frequency-magnitude formula was derived from the solution ofthe generalized logistic equation as an asymptotic case in approximation oflarge magnitudes. To illustrate how the found solution of the generalizedlogistic equation works, it was used to approximate the observed cumulativedistribution of earthquakes in four different geological provinces: the CentralAtlantic (40N-25N, 5W-35W), Canary Islands, Magellan Mountains (20N-9S,148E-170E), and the Sea of Japan. This approximation showed the excellent fitbetween the theoretical curves and observed data for earthquake magnitudes1<m<9.

Derivation of the Gutenberg-Richter Empirical Formula from the Solution of the Generalized Logistic Equation