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The Maximum Likelihood Estimator of b-Value for Mainshocks

Istituto Nazionale di Geofisica e Vulcanologia, Roma
via di Vigna Murata, 605
00143 Roma, Italy
lombardi{at}ingv.it

Considering the magnitudes of events in a catalog as independent and exponentially distributed random variables, in agreement with the Gutenberg–Richter law, the statistical significance of the difference between the maximum likelihood estimators of the b-value for mainshocks (b_ms) and for all events (b_all) is discussed. It is shown that, as a consequence of their definition, the mainshocks do not entirely satisfy the Gutenberg–Richter law and that b_ms has been frequently estimated as lower than b_all because of an incorrect use of the maximum likelihood method.