We have written a new equation to study the statistics of earthquake distributions. We call this equation “the generalized logistic equation”. The Gutenberg-Richter frequency-magnitude formula was derived from the solution of the generalized logistic equation as an asymptotic case for the approximation of large magnitudes. To illustrate how the solution of the generalized logistic equation works, it was used to approximate the observed cumulative distribution of earthquakes in four different geological provinces: the Central Atlantic (40N - 25N, 5W - 35W), Canary Islands, Magellan Mountains (20N - 9S, 148E - 170E), and the Sea of Japan. This approximation showed an excellent correlation between the theoretical curves and observed data for earthquakes of magnitudes 1 < m < 9.
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