Maximum likelihood estimation of the nonextensive parameters of the earthquake cumulative magnitude distribution

Recently, interest in the application of nonextensive models to the earthquake cumulative magnitude distribution (ECMD) has been increasing. Nonextensivity in seismicity leads to a new form of the cumulative distribution of earthquake magnitudes, of which the Gutenberg-Richter law can be considered as a particular case. The present study deals with the mathematical problem of estimation of the nonextensive parameters of the ECMD by means of the maximum likelihood method.