  The distribution of seismic moment is of capital interest to evaluate
earthquake hazard, in particular regarding the most extreme events. We make use
of likelihood-ratio tests to compare the simple Gutenberg-Richter power-law
distribution with two statistical models that incorporate an exponential tail:
the so-called tapered Gutenberg-Richter and the truncated gamma, when fitted to
the global CMT earthquake catalog. The outcome is that the truncated gamma
model outperforms the other two models. If simulated samples of the truncated
gamma are reshuffled in order to mimic the time occurrence of the order
statistics of the empirical data, this model turns out to be able to explain
the empirical data both before and after the great Sumatra-Andaman earthquake
of 2004.
